Standing Waves for Periodic Discrete Nonlinear Schrdinger Equations with Asymptotically Linear Terms  

作　　者：Wen-xiong Chen Min-bo Yang 

机构地区：[1]School of Mathematical Science,Huaqiao University,Quanzhou 362021,Fujian,China [2]Department of Mathematics,Zhejiang Normal University,321004 Jinhua,China

出　　处：《Acta Mathematicae Applicatae Sinica》2012年第2期351-360,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 10971194);the Science Foundation of Huaqiao University,the Natural Science Foundation of Zhejiang Province (No. Y7080008,No. R6090109);Zhejiang Innovation Project (No. T200905)

摘　　要：In this paper we study the existence of nontrivial solutions for the periodic discrete nonlinear equation Lun-un=ωfn（un）,where Lun=an＋1un＋an-1un-1＋bnunis the discrete Laplacian in one spatial dimension. The given real-valued sequences an, bn are assumed to be N-periodic in n, i.e., an＋N =an, bn＋N = bn. The nonlinearity fn（t） is N-periodic in n and asymptotically linear at infinity. We show that, if ω is in the spectrum gap of L, there is a nontrivial solution. The proof is based on the strongly indefinite functional critical points theorem developed recently.In this paper we study the existence of nontrivial solutions for the periodic discrete nonlinear equation Lun-un=ωfn（un）,where Lun=an＋1un＋an-1un-1＋bnunis the discrete Laplacian in one spatial dimension. The given real-valued sequences an, bn are assumed to be N-periodic in n, i.e., an＋N =an, bn＋N = bn. The nonlinearity fn（t） is N-periodic in n and asymptotically linear at infinity. We show that, if ω is in the spectrum gap of L, there is a nontrivial solution. The proof is based on the strongly indefinite functional critical points theorem developed recently.

关 键 词：discrete Schrodinger equation critical point LINKING 

分 类 号：O241.7[理学—计算数学] O175.23[理学—数学]