摘要：
In this paper, we investigate the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems. By using fountain theorem due to Zou, we obtain two new criteria for guaranteeing that second order Hamiltonian systems have infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved.
摘要：
We study a nonlocal boundary value problem of impulsive fractional differential equations. By means of a fixed point theorem due to O'Regan, we establish sufficient conditions for the existence of at least one solution of the problem. For the illustration of the main result, an example is given. Copyright 2011 Liu Yang and Haibo Chen.
期刊：
Journal of Applied Mathematics and Computing,2011年35(1-2):323-340 ISSN：1598-5865
通讯作者：
Sun, J.(sunjuntao2008@163.com)
作者机构：
[Yang, Liu; Chen, Haibo; Sun, Juntao] Department of Mathematics, Central South University, Changsha, Hunan 410075, China;[Yang, Liu] Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, China
通讯机构：
[Juntao Sun] D;Department of Mathematics, Central South University, Changsha, People’s Republic of China
关键词：
Boundary value problems;Critical points;Impulsive differential equations;Variational methods
摘要：
Many dynamical systems have impulsive dynamical behaviors due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations. In this paper, we study the existence and multiplicity of solutions for fourth-order impulsive differential equations. By using the variational methods and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one nontrivial solution, infinitely many distinct solutions under some different conditions, respectively. Some examples are given in this paper to illustrate the feasibilities of our main results.
期刊：
Abstract and Applied Analysis,2011年2011:1-15 ISSN：1085-3375
通讯作者：
Chen, Haibo
作者机构：
[Chen, Haibo; Yang, Liu] Cent S Univ, Dept Math, Changsha 421008, Hunan, Peoples R China.;[Yang, Liu] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Chen, Haibo] C;Cent S Univ, Dept Math, Changsha 421008, Hunan, Peoples R China.
关键词：
We investigate the existence and multiplicity of periodic solutions for a class of second-order differential systems with impulses. By using variational methods and critical point theory;we obtain such a system possesses at least one nonzero;two nonzero;or infinitely many periodic solutions generated by impulses under different conditions;respectively. Recent results in the literature are generalized and significantly improved. Published: 2011 First available in Project Euclid: 12 August 2011 zbMATH: 1253.34046 MathSciNet: MR2800077 Digital Object Identifier: 10.1155/2011/310957
摘要：
In this paper, we study the Schrodinger-Poisson system {-Delta u + V(x)u + lambda phi(x)u = K(x)f(u), in R(3), -Delta phi = u(2), u > 0, in R(3), (SP) and prove the existence of positive solutions for system (SP) when the nonlinearity f has growth at most linear for lambda small, allowing the potential V(x) to vanish at infinity. In addition, also we obtain the nonexistence of a nontrivial positive solution for lambda >= 1/4. (C) 2010 Elsevier Ltd. All rights reserved.
