Journal of Applied Mathematics
Volume 2013 (2013), Article ID 431672, 9 pages
http://dx.doi.org/10.1155/2013/431672
Research Article

Existence of Solutions for a Modified Nonlinear Schrödinger System

Yujuan Jiao1 and Yanli Wang2

1College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, China
2School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received 8 April 2013; Accepted 18 June 2013

Academic Editor: Renat Zhdanov

Copyright © 2013 Yujuan Jiao and Yanli Wang. 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 are concerned with the following modified nonlinear Schrödinger system: ,   ,   ,   ,   ,   ,   , where ,   ,   ,   is the critical Sobolev exponent, and    is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system.