Abstract and Applied Analysis
Volume 2013 (2013), Article ID 317139, 11 pages
Research Article

Ground State Solutions for the Periodic Discrete Nonlinear Schrödinger Equations with Superlinear Nonlinearities

Ali Mai1,2,3 and Zhan Zhou1,2

1School of Mathematics and Information Science, Guangzhou University, Guangdong, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangdong, Guangzhou 510006, China
3Department of Applied Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, China

Received 31 December 2012; Revised 22 March 2013; Accepted 24 March 2013

Academic Editor: Yuming Chen

Copyright © 2013 Ali Mai and Zhan Zhou. 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.


We consider the periodic discrete nonlinear Schrödinger equations with the temporal frequency belonging to a spectral gap. By using the generalized Nehari manifold approach developed by Szulkin and Weth, we prove the existence of ground state solutions of the equations. We obtain infinitely many geometrically distinct solutions of the equations when specially the nonlinearity is odd. The classical Ambrosetti-Rabinowitz superlinear condition is improved.