Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory ca...Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.展开更多
In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation ...In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.展开更多
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.展开更多
This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be converg...This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.展开更多
A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential ...A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.展开更多
This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined space.First, the study derivative analytical stability and synchronization conditions for the asymmetrically...This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined space.First, the study derivative analytical stability and synchronization conditions for the asymmetrically coupled system in an unconfined space, which are then validated through numerical simulations. Simulation results show that asymmetric coupling has a significant impact on synchronization conditions. Moreover, it is observed that irrespective of whether the system is confined, an increase in coupling asymmetry leads to a hastened synchronization pace. Additionally, the study examines the effects of boundaries on the system's collective behaviors via numerical experiments. The presence of boundaries ensures the system's stability and synchronization, and reducing these boundaries can expedite the synchronization process and amplify its effects. Finally, the study reveals that the system's output amplitude exhibits stochastic resonance as the confined boundary size increases.展开更多
The Berry-Tabor(BT)conjecture is a famous statistical inference in quantum chaos,which not only establishes the spectral fluctuations of quantum systems whose classical counterparts are integrable but can also be used...The Berry-Tabor(BT)conjecture is a famous statistical inference in quantum chaos,which not only establishes the spectral fluctuations of quantum systems whose classical counterparts are integrable but can also be used to describe other wave phenomena.In this paper,the BT conjecture has been extended to Lévy plates.As predicted by the BT conjecture,level clustering is present in the spectra of Lévy plates.The consequence of level clustering is studied by introducing the distribution of nearest neighbor frequency level spacing ratios P(r),which is calculated through the analytical solution obtained by the Hamiltonian approach.Our work investigates the impact of varying foundation parameters,rotary inertia,and boundary conditions on the frequency spectra,and we find that P(r)conforms to a Poisson distribution in all cases.The reason for the occurrence of the Poisson distribution in the Lévy plates is the independence between modal frequencies,which can be understood through mode functions.展开更多
In this paper,we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations.Under some suitable conditions,we give ...In this paper,we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations.Under some suitable conditions,we give the gradient estimates of these maps and establish a Liouville type result.展开更多
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol...In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.展开更多
This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length.The background charge in the Poisson equation is a piecewise consta...This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length.The background charge in the Poisson equation is a piecewise constant function.The structural stability of the steady transonic shock solution is obtained by the monotonicity argument.Furthermore,this transonic shock is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.One of the crucial ingredients of the analysis is to establish the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions.展开更多
In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p...In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.展开更多
In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exp...In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exponent from the Schrödinger cocycle in[24]to a Szegö cocycle.展开更多
We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-l...We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.展开更多
In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The prop...In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.展开更多
This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theor...This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.展开更多
The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappin...The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions.Then,using these results,we establish five Landau-type theorems for subclasses of polyharmonic mappings F and L(F),where F has bounded length distortion and L is a differential operator.展开更多
The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order...The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.展开更多
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.展开更多
In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this p...In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.展开更多
Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som...Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.展开更多
基金supported by the National Natural Science Foundation of China(11871238,11931019,12371486)。
文摘Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.
基金Supported by the Jiangsu Higher School Undergraduate Innovation and Entrepreneurship Training Program(202311117078Y)。
文摘In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
基金partially supported by the NSFC(11421061,12271507)the Natural Science Foundation of Shanghai(15ZR1403900)。
文摘This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52171251,U2106225,and 52231011)Dalian Science and Technology Innovation Fund (Grant No.2022JJ12GX036)。
文摘A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.
基金Project supported by the Natural Science Foundation of Shandong Province of China for the Youth (Grant No. ZR2023QA102)。
文摘This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined space.First, the study derivative analytical stability and synchronization conditions for the asymmetrically coupled system in an unconfined space, which are then validated through numerical simulations. Simulation results show that asymmetric coupling has a significant impact on synchronization conditions. Moreover, it is observed that irrespective of whether the system is confined, an increase in coupling asymmetry leads to a hastened synchronization pace. Additionally, the study examines the effects of boundaries on the system's collective behaviors via numerical experiments. The presence of boundaries ensures the system's stability and synchronization, and reducing these boundaries can expedite the synchronization process and amplify its effects. Finally, the study reveals that the system's output amplitude exhibits stochastic resonance as the confined boundary size increases.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China(Grant No.2021MS01004)the Innovation Program for Graduate Education of Inner Mongolia University(Grant No.11200-5223737).
文摘The Berry-Tabor(BT)conjecture is a famous statistical inference in quantum chaos,which not only establishes the spectral fluctuations of quantum systems whose classical counterparts are integrable but can also be used to describe other wave phenomena.In this paper,the BT conjecture has been extended to Lévy plates.As predicted by the BT conjecture,level clustering is present in the spectra of Lévy plates.The consequence of level clustering is studied by introducing the distribution of nearest neighbor frequency level spacing ratios P(r),which is calculated through the analytical solution obtained by the Hamiltonian approach.Our work investigates the impact of varying foundation parameters,rotary inertia,and boundary conditions on the frequency spectra,and we find that P(r)conforms to a Poisson distribution in all cases.The reason for the occurrence of the Poisson distribution in the Lévy plates is the independence between modal frequencies,which can be understood through mode functions.
文摘In this paper,we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations.Under some suitable conditions,we give the gradient estimates of these maps and establish a Liouville type result.
文摘In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.
基金supported by the National Natural Science Foundation of China(11871134,12171166)the Fundamental Research Funds for the Central Universities(DUT23LAB303)。
文摘This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length.The background charge in the Poisson equation is a piecewise constant function.The structural stability of the steady transonic shock solution is obtained by the monotonicity argument.Furthermore,this transonic shock is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.One of the crucial ingredients of the analysis is to establish the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions.
基金partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100523,KJQN202000536)the National Natural Science Foundation of China(12001074)+3 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0606)supported by the National Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0278)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100503)the Research Project of Chongqing Education Commission(CXQT21014)。
文摘In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.
文摘In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exponent from the Schrödinger cocycle in[24]to a Szegö cocycle.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61877054,12031004,and 12271474).
文摘We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.
基金supported partly by the National Natural Science Foundation of China(11926201,12171050)the National Science Foundation of Guangdong Province(2018A030313508)。
文摘In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.62363005)the Jiangxi Provincial Natural Science Foundation(Grant Nos.20161BAB212032 and 20232BAB202034)the Science and Technology Research Project of Jiangxi Provincial Department of Education(Grant Nos.GJJ202602 and GJJ202601)。
文摘This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)supported by the Youth Innovation Foundation of Shenzhen Polytechnic University(6024310023K)。
文摘The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions.Then,using these results,we establish five Landau-type theorems for subclasses of polyharmonic mappings F and L(F),where F has bounded length distortion and L is a differential operator.
基金Project supported by the National Natural Science Foundation of China (Grants Nos.12375031 and 11905068)the Natural Science Foundation of Fujian Province, China (Grant No.2023J01113)the Scientific Research Funds of Huaqiao University (Grant No.ZQN-810)。
文摘The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
基金partially supported by the NSFC(12271269)the Fundamental Research Funds for the Central Universitiespartially supported by the Fundamental Research Funds for the Central Universities(2021YJSB006)。
文摘In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.
基金supported by the National Key Research and Development Program of China(2020YFA0712900)the National Natural Science Foundation of China(12371093,12071197,12122102 and 12071431)+2 种基金the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the Fundamental Research Funds for the Central Universities(2233300008 and lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
