In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivia...In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.展开更多
By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′...By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.展开更多
This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″...This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.展开更多
The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presente...The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presented. The special case when φ(s) = |s|p-2 s,p > 1 is also considered. Our analysis is based on the nonlinear alternative of Leray-Schauder and barrier strips.展开更多
In this paper, we study the existence of solutions to a three-point boundary value problem with nonlinear growth. Sufficient conditions for the existence of solutions to the system in the resonance and non-resonance c...In this paper, we study the existence of solutions to a three-point boundary value problem with nonlinear growth. Sufficient conditions for the existence of solutions to the system in the resonance and non-resonance cases are established by employing Leray-Schauder continuation theorem and the coincidence degree theory.展开更多
本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间...本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.展开更多
基金This work was supported by Key Academic Discipline of Zhejiang Province of China(2005)the Natural Science Foundation of Zhejiang Province of China(Y605144)the Education Department of Zhejiang Province of China(20051897).
文摘In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.
文摘By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Y605144)
文摘This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.
基金the National Science Function of China (19971037)
文摘The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presented. The special case when φ(s) = |s|p-2 s,p > 1 is also considered. Our analysis is based on the nonlinear alternative of Leray-Schauder and barrier strips.
文摘In this paper, we study the existence of solutions to a three-point boundary value problem with nonlinear growth. Sufficient conditions for the existence of solutions to the system in the resonance and non-resonance cases are established by employing Leray-Schauder continuation theorem and the coincidence degree theory.
文摘本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.
