Standing waves to discrete vector nonlinear Schrödinger equation

Abstract

The purpose of this paper is to study a class of periodic discrete vector nonlinear Schrödinger equation. By using the critical point theory for strongly indefinite problems developed by Ding (Interdisciplinary Mathematical Sciences, World Scientific, Hackensack, NJ, 2007), we prove the existence of non-trivial standing waves for the vector equation with periodic or asymptotically periodic nonlinearities.

Keywords:

• discrete vector Schrödinger equation
• standing waves
• critical point theory

2000 Mathematics Subject Classification::

• 35Q55
• 35Q51
• 39A12
• 39A70

Acknowledgement

This work was supported by ZJNSF (Y7080008, R6090109) and NSFC (10971194).