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
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
In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is ...In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is considered as Lipschitz condition or non-Lipschitz case, respectively. The results are a consequence of application of different fixed point theorems, namely, the contraction mapping principle, the Leray-Schauder alternative theorem and Matkowski’s fixed point technique.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.
文摘由构造合适的 Banach space.an ，存在定理为第三顺序的边界价值问题u'在线性生长的一个条件下面被建立“(t) +f ( t ， u (t)，t'(t)， u ”(t)) =0,0t1 ， u ( 0 )=u'( 0 )=u'( 1 ) =0 ，在非线性的条款包含未知 function.In 的第一和第二衍生物的地方这条定理非线性的条款 f ( t ， u ， v ， w )可能在 t=0 和 t=1.The 单个主要成分 Leray-Schauder 非线性的选择。
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.
基金supported by the National Natural Science Foundation of China(No.11501507)the Natural Science Foundation of Zhejiang Province(No.LY19A010013)
文摘In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is considered as Lipschitz condition or non-Lipschitz case, respectively. The results are a consequence of application of different fixed point theorems, namely, the contraction mapping principle, the Leray-Schauder alternative theorem and Matkowski’s fixed point technique.
