Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 57676, 7 pages
Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential
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.
This paper is concerned with the nonlinear Schrödinger
equation with an unbounded potential , , where , and . The potential is bounded
from below and satisfies as . From variational calculus and a
compactness lemma, the existence of standing waves and their
orbital stability are obtained.