二阶离散Hamiltonian系统的多重变号周期解(英文)  

Multiple Sign-changing Periodic Solutions of Second Order Discrete Hamiltonian Systems

作　　者：贺铁山[1] 陈文革[2] 雷友发[1] 

机构地区：[1]仲恺农业工程学院计算科学系,广东广州510225 [2]华南理工大学理学院,广东广州510640

出　　处：《四川师范大学学报（自然科学版）》2010年第4期462-466,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：supported by Science and Technology Plan Foundation of Guangdong Province(2006J1-C0341);Science Foundation of the Education Department of Fujian Province(JA06035)~~

摘　　要：研究了二阶非自治离散Hamilton系统多重变号周期解的存在性问题.在非线性项是奇函数的条件下,将这类Ham-ilton系统的变号周期解转化为定义在一个适当空间上泛函的临界点,然后利用Morse理论中的三临界点定理,建立了此类系统至少2个变号周期解的存在性结果,并举例说明了所获得的主要结果是有效的.In this paper, we investigate the existence of multiple signchanging periodic solutions for second order nonautonomous discrete Hamiltonian system. Under the condition that the nonlinearity is an odd function, we convert signchanging periodic solutions of the system into the critical points of a functional defined on a proper space, and prove that there exist at least two different signchanging periodic solutions. The approach used here is based on a 3 critical points theorem in the Morse theory. An illustrative example is given to demonstrate the effectiveness of the obtained main result.

关 键 词：变号周期解 离散HAMILTON系统 临界点 

分 类 号：O175.7[理学—数学]