Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 57676, 7 pages
doi:10.1155/JAMSA/2006/57676

Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential

Guanggan Chen,1 Jian Zhang,2 and Yunyun Wei3

1College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
3College of Information Management, Chengdu University of Technology, Chengdu 610059, China

Received 26 August 2004; Revised 20 October 2004; Accepted 9 November 2004

Copyright © 2006 Guanggan Chen et al. 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

This paper is concerned with the nonlinear Schrödinger equation with an unbounded potential iϕt=−Δϕ+V(x)ϕ−μ|ϕ|p−1ϕ−λ|ϕ|q−1ϕ, x∈ℝN, t≥0, where μ>0, λ>0, and 1<p<q<1+4/N. The potential V(x) is bounded from below and satisfies V(x)→∞ as |x|→∞. From variational calculus and a compactness lemma, the existence of standing waves and their orbital stability are obtained.