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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 539639, 10 pages
http://dx.doi.org/10.1155/2014/539639
Research Article

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.