The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary ...The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.展开更多
By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed w...By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.展开更多
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
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e...The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.展开更多
A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value prob...A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.展开更多
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan...Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.展开更多
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0...The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems ar...The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied.展开更多
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 ...Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.展开更多
This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that...The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and λ > 0 is small enough; (ii) f is sublinear at infinity and λ > 0 is large enough. Their proofs are based on fixed point theorems in cones.展开更多
In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t）...The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t） is the boundary value of the unknown function ψ（z） holomorphic in ｜z｜ 〈 1 with single-valued continuous p√ψ＋（t） on L.展开更多
The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching...The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.展开更多
In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansio...In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained.展开更多
In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,...In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,we get the solutions of R m（m〉0） Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m（m〉0） Riemann boundary value problems for harmonic functions and bi-harmonic functions.展开更多
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = ...In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f.展开更多
文摘The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.
文摘By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.
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The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.
文摘A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.
基金supported by the NSF of Hebei Province(A2022208007)the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)。
文摘Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
文摘The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
基金The project supported by the National Natural Science Foundation of China
文摘The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied.
基金Supported by the Natural Science Foundation of Hunan Province（06JJ50008） Supported by the Natural Science Foundation of Guangdong Province（7004569）
文摘Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.
文摘This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Supported by Natural Science Foundation of ChinaFoundation of Key Teacher of University of Education Ministry
文摘The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and λ > 0 is small enough; (ii) f is sublinear at infinity and λ > 0 is large enough. Their proofs are based on fixed point theorems in cones.
基金Supported by the Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
文摘The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t） is the boundary value of the unknown function ψ（z） holomorphic in ｜z｜ 〈 1 with single-valued continuous p√ψ＋（t） on L.
基金Supported by the NNSF of China（10901003） Supported by the Natural Science Foundation from the Education Bureau of Anhui Province（KJ2011A135）
文摘The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.
文摘In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained.
基金Supported by NSF of China (11171260)RFDP of Higher Eduction of China (20100141110054)
文摘In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,we get the solutions of R m（m〉0） Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m（m〉0） Riemann boundary value problems for harmonic functions and bi-harmonic functions.
文摘In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
基金supported by the National Natural Science Foundation of China (11071149, 10771128)the NSF of Shanxi Province (2006011002, 2010011001-1)
文摘In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f.
