Abstract and Applied Analysis
Volume 2014, Article ID 539639, 10 pages
http://dx.doi.org/10.1155/2014/539639
Existence of Nontrivial Solutions for Periodic Schrödinger Equations with New Nonlinearities
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
Received 13 April 2014; Accepted 29 May 2014; Published 15 June 2014
Academic Editor: Mihai Mihǎilescu
Copyright © 2014 Shaowei Chen and Dawei Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the Schrödinger equation: , where is -periodic and is -periodic in the -variables; is in a gap of the spectrum of the operator . We prove that, under some new assumptions for , this equation has a nontrivial solution. Our assumptions for the nonlinearity are very weak and greatly different from the known assumptions in the literature.