Notes on gap solitons for periodic discrete nonlinear Schrodinger equations

摘要

Consider a class of periodic discrete Schrodinger equations Under the condition of.. n (un) =.. n| un| 2un, by applying the linking theorem, Pankov obtained the existence of gap solitons. Pankov's result was then generalized to various type of nonlinear function fn, but most of studying works were concentrated on the case of.. n(t) = O(| t| s1) as t. 0(s1. 1). In this paper, by ingeniously using Ekeland variational principle, for the nonlinearity which meets.. n(t) = O(| t| s1) as t. 0 (s1. (0, 1)), we obtain the existence of gap solitons, which supplements the existing ones and gives a positive answer in part to the open problem proposed by Pankov.