This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive...This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.展开更多
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0...We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0, x′（0）-∑i=1^m2 βi x′（ηi） = 0, x′（1）=0,where 0 ≤ ai≤∑i=1^m1 αi 〈 1, i = 1, 2, ···, m1, 0 〈 ξ1〈 ξ2〈 ··· 〈 ξm1〈 1, 0 ≤βj≤∑i^m2=1βi〈1,J=1,2, ···, m2, 0 〈 η1〈 η2〈 ··· 〈 ηm2〈 1. And we obtain some necessa βi 〈=11, j = 1,ry and sufficient conditions for the existence of C^1[0, 1] and C^2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f（t, x, y）may be singular at x, y, t = 0 and/or t = 1.展开更多
This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution...The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.展开更多
In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positiv...In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature.展开更多
The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding ste...The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.展开更多
In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem ha...This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem has at least two positive solutions for 0 < λ < λ~* , at least one positive solution for λ = λ~* and no solution forλ > λ~* by using the upper and lower solutions method and fixed point theory.展开更多
This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)...This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 >0 and c～2+d～2>0,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.展开更多
In this paper,using the existence and comparison result for the quasi-monotone increasing system developed by C V Pao,the upper and lower solutions principle and an iterative method,we investigate the existence of the...In this paper,using the existence and comparison result for the quasi-monotone increasing system developed by C V Pao,the upper and lower solutions principle and an iterative method,we investigate the existence of the positive solutions of the Volterra-Lotka cooperating model.展开更多
This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem a...This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.展开更多
In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term witho...In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.展开更多
Making use of upper and lower solutions and analytical method, the author studies theexistence of positive solution for the singular equation x + f(t, z) = 0 satisfying nonlinear boundary conditions: x (0) = 0, h(x (1...Making use of upper and lower solutions and analytical method, the author studies theexistence of positive solution for the singular equation x + f(t, z) = 0 satisfying nonlinear boundary conditions: x (0) = 0, h(x (1), x’ (1)) = 0, g (z (0), x’(0)) = 0, and x (1) = 0,which extends the result of J. V. Baxley.展开更多
Battery safety is influenced by various factors,with thermal runaway being one of the most significant concerns.While most studies have concentrated on developing one-time,self-activating mechanism for thermal protect...Battery safety is influenced by various factors,with thermal runaway being one of the most significant concerns.While most studies have concentrated on developing one-time,self-activating mechanism for thermal protection,such as temperature-responsive electrodes,and thermal-shutdown separators,these methods only provide irreversible protection.Recently,reversible temperature-sensitive electrolytes have emerged as promising alternatives,offering both thermo-reversibility and self-protective properties.However,further research is crucial to fully understand these thermal-shutdown electrolytes.In this study,we propose lower critical solution temperature(LCST)phase behavior poly(benzyl methacrylate)/imidazolium-based ionic liquid mixtures to prepare temperature-sensitive electrolytes that provide reversible thermal shutdown protection of batteries.This electrolyte features an appropriate protection temperature(~105℃)and responds quickly within a 1 min at 105℃,causing cells to hardly discharge as the voltage suddenly drops to 3.38 V,and providing efficient thermal shutdown protection within 30 min.Upon cooling back to room temperature,the battery regains its original performance.Additionally,the electrolyte exhibits excellent cycling stability with the capacity retention of the battery is 91.6%after 500 cycles.This work provides a viable solution for preventing batteries from thermal runaway triggered by overheating.展开更多
This paper considers the travelling wave fronts to a delayed lattice differential equation. The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions deve...This paper considers the travelling wave fronts to a delayed lattice differential equation. The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions developed by J Wu and X Zou in [6]. This work extends that of [4] in a general class of nonlinear terms.展开更多
We study a class of semilinear periodic-parabolic boundary value problem with small diffusion coefficients,give its asymptotic behavior when the diffusion cofficients go to limit zero.
An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower sol...An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.展开更多
文摘This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
基金supported by the National Science Foundation of Shandong Province(ZR2009AM004)
文摘We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0, x′（0）-∑i=1^m2 βi x′（ηi） = 0, x′（1）=0,where 0 ≤ ai≤∑i=1^m1 αi 〈 1, i = 1, 2, ···, m1, 0 〈 ξ1〈 ξ2〈 ··· 〈 ξm1〈 1, 0 ≤βj≤∑i^m2=1βi〈1,J=1,2, ···, m2, 0 〈 η1〈 η2〈 ··· 〈 ηm2〈 1. And we obtain some necessa βi 〈=11, j = 1,ry and sufficient conditions for the existence of C^1[0, 1] and C^2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f（t, x, y）may be singular at x, y, t = 0 and/or t = 1.
文摘This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
文摘The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.
文摘In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature.
基金The project is supported by National Natural Science Foundation of China (10071026)
文摘The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.
文摘In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
文摘This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem has at least two positive solutions for 0 < λ < λ~* , at least one positive solution for λ = λ~* and no solution forλ > λ~* by using the upper and lower solutions method and fixed point theory.
文摘This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 >0 and c～2+d～2>0,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.
文摘In this paper,using the existence and comparison result for the quasi-monotone increasing system developed by C V Pao,the upper and lower solutions principle and an iterative method,we investigate the existence of the positive solutions of the Volterra-Lotka cooperating model.
文摘This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.
基金supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of ChinaNatural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of ChinaNational Natural Science Foundation of China (11101298)
文摘In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.
文摘Making use of upper and lower solutions and analytical method, the author studies theexistence of positive solution for the singular equation x + f(t, z) = 0 satisfying nonlinear boundary conditions: x (0) = 0, h(x (1), x’ (1)) = 0, g (z (0), x’(0)) = 0, and x (1) = 0,which extends the result of J. V. Baxley.
基金funded by the National Natural Science Foundation of China(no.22075155)the Zhejiang Provincial Natural Science Foundation of China(No.LY24B030002)+2 种基金Ningbo Natural Science Foundation(2023J089)the China Scholarship Council(CSC)the Ningbo Science and Technology Bureau(2024QL036).
文摘Battery safety is influenced by various factors,with thermal runaway being one of the most significant concerns.While most studies have concentrated on developing one-time,self-activating mechanism for thermal protection,such as temperature-responsive electrodes,and thermal-shutdown separators,these methods only provide irreversible protection.Recently,reversible temperature-sensitive electrolytes have emerged as promising alternatives,offering both thermo-reversibility and self-protective properties.However,further research is crucial to fully understand these thermal-shutdown electrolytes.In this study,we propose lower critical solution temperature(LCST)phase behavior poly(benzyl methacrylate)/imidazolium-based ionic liquid mixtures to prepare temperature-sensitive electrolytes that provide reversible thermal shutdown protection of batteries.This electrolyte features an appropriate protection temperature(~105℃)and responds quickly within a 1 min at 105℃,causing cells to hardly discharge as the voltage suddenly drops to 3.38 V,and providing efficient thermal shutdown protection within 30 min.Upon cooling back to room temperature,the battery regains its original performance.Additionally,the electrolyte exhibits excellent cycling stability with the capacity retention of the battery is 91.6%after 500 cycles.This work provides a viable solution for preventing batteries from thermal runaway triggered by overheating.
基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry(20030917)
文摘This paper considers the travelling wave fronts to a delayed lattice differential equation. The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions developed by J Wu and X Zou in [6]. This work extends that of [4] in a general class of nonlinear terms.
文摘We study a class of semilinear periodic-parabolic boundary value problem with small diffusion coefficients,give its asymptotic behavior when the diffusion cofficients go to limit zero.
基金Supported by the National Natural Science Foundation of China（11371368） Supported by the Natural Science Foundation of Hebei Province（A2013506012） Supported by the Foundation of Shijiazhuang Mechanical Engineering College（JCB1201, YJJXM13008）
文摘An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
