非线性差分方程周期解与次调和解的存在性  

Existence of Periodic and Subharmonic Solutions for Nonlinear Difference Equations

作　　者：范瑶颖 FAN Yao-ying(School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《五邑大学学报（自然科学版）》2017年第1期7-13,共7页Journal of Wuyi University(Natural Science Edition)

摘　　要：本文首先建立二阶差分方程的变分泛函,然后将周期解的存在性转化为相应变分泛函的临界点的存在性,再利用临界点理论中的环绕定理得到该泛函临界点的存在性,证明方程至少有两个非平凡周期解的存在性.本文结果推广了陈等2008年所得的相关结论.In this paper, we study second-order suplinear difference equations.First, by establishing a suitable variational framework, we turn the periodic solution problem into a critical point problem of corresponding functional.Next, by using the Linking Theorem of critical point theory, we obtain the existence of a critical point of the functional and prove the existence of at least two nontrivial periodic solutions.The results generalize Chen＇s related conclusion reached in 2008.

关 键 词：差分方程 周期解 存在性 环绕定理 

分 类 号：O175.7[理学—数学]