About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 786736, 7 pages
http://dx.doi.org/10.1155/2013/786736
Research Article

Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity

Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

Received 2 July 2013; Accepted 21 November 2013

Academic Editor: Stepan Agop Tersian

Copyright © 2013 Hongbo Zhu. 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 study the following nonlinear Schrödinger equation , where the potential vanishes at infinity. Working in weighted Sobolev space, we obtain the ground states of problem under a Nahari type condition. Furthermore, if are radically symmetric with respect to , it is shown that problem has a positive solution with some more general growth conditions of the nonlinearity. Particularly, if , then the growth restriction in Ambrosetti et al. (2005) can be relaxed to , where if .