摘要：
In this article, we are concerned with a class of fourth-order elliptic equations with sublinear perturbation and steep potential well. By using variational methods, we obtain that such equations admit at least two nontrivial solutions. We also explore the phenomenon of concentration of solutions.
期刊：
Abstract and Applied Analysis,2014年2014(SI62):1-6 ISSN：1085-3375
通讯作者：
Yang, Liu
作者机构：
[Yang, Liu] Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Yang, Liu] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
We consider the existence of infinitely many classical solutions to a class of impulsive differential equations with Dirichlet boundary value condition. Our main tools are based on variant fountain theorems and variational method. We study the case in which the nonlinearity is sublinear. Some recent results are extended and improved. Published: 2014 First available in Project Euclid: 2 October 2014 zbMATH: 07022474 MathSciNet: MR3206792 Digital Object Identifier: 10.1155/2014/487952
摘要：
We consider the existence of infinitely many classical solutions to a class of impulsive differential equations with Dirichlet boundary value condition. Our main tools are based on variant fountain theorems and variational method. We study the case in which the nonlinearity is sublinear. Some recent results are extended and improved.
期刊：
Abstract and Applied Analysis,2014年2014(SI17):1-7 ISSN：1085-3375
通讯作者：
Yang, Liu
作者机构：
[Yang, Liu] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Yang, Liu] H;Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.
关键词：
We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory;we obtain that such equations possess infinitely homoclinic solutions. Published: 2014 First available in Project Euclid: 3 October 2014 zbMATH: 07022386 MathSciNet: MR3226194 Digital Object Identifier: 10.1155/2014/435125
通讯机构：
[Luo, Zhenguo] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses;by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously. Published: 2014 First available in Project Euclid: 2 October 2014 zbMATH: 07023067 MathSciNet: MR3193546 Digital Object Identifier: 10.1155/2014/785653
期刊：
Journal of Applied Mathematics,2014年2014(Pt.3):592543:1-592543:21 ISSN：1110-757X
通讯作者：
Luo, Zhenguo
作者机构：
[Luo, Liping; Gao, Zhenghui; Zeng, Yunhui; Yang, Liu; Luo, Zhenguo] Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.;[Luo, Zhenguo] Natl Univ Def Technol, China Dept Math, Changsha 410073, Hunan, Peoples R China.
通讯机构：
[Luo, Zhenguo] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated;where we assume the model of patches with a barrier only as far as the prey population is concerned;whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional;a set of easily verifiable sufficient conditions are obtained to guarantee the existence;uniqueness;and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application;we also give two examples to illustrate the feasibility of our main results. Published: 2014 First available in Project Euclid: 2 March 2015 zbMATH: 07010692 MathSciNet: MR3191132 Digital Object Identifier: 10.1155/2014/592543
摘要：
An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.
作者机构：
[Luo, Liping; Yang, Liu; Luo, Zhenguo] Hengyang Normal Univ, Hengyang, Peoples R China.
通讯机构：
[Yang, Liu] H;Hengyang Normal Univ, Hengyang, Peoples R China.
关键词：
Hamiltonian System;Homoclinic Orbit;Weighted Sobolev Space;Homoclinic Solution;Positive Continuous Function
摘要：
We investigate the existence of infinitely many fast homoclinic solutions for a class of second-order nonautonomous systems. Our main tools are based on the variant fountain theorem. A criterion guaranteeing that the second-order system has infinitely many fast homoclinic solutions is obtained. Recent results from the literature are generalized and significantly improved.
期刊：
Journal of Applied Mathematics and Computing,2013年42(1-2):89-102 ISSN：1598-5865
通讯作者：
Yang, L.(yangliu19731974@yahoo.com.cn)
作者机构：
[Yang, Liu; Luo, Liping; Luo, Zhenguo] Department of Mathematics and Computing Sciences, Hengyang Normal University, Hengyang, People’s Republic of China;[Chen, Haibo] Department of Mathematics, Central South University, Changsha, People’s Republic of China
通讯机构：
[Liu Yang] D;Department of Mathematics and Computing Sciences, Hengyang Normal University, Hengyang, People’s Republic of China
摘要：
In this paper, we investigate the positive solutions for a class of nonlinear q-fractional boundary value problem. We not only obtain the existence and uniqueness of positive solutions, but also establish the iterative schemes for approximating the solutions, which is benefit for computation and application.
