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Abstract and Applied Analysis
Volume 2014, Article ID 646145, 6 pages
http://dx.doi.org/10.1155/2014/646145
Research Article

versus Local Minimizers

Department of Mathematics, Fujian Normal University, Fuzhou 350117, China

Received 18 March 2014; Accepted 9 April 2014; Published 28 April 2014

Academic Editor: Jianqing Chen

Copyright © 2014 Yansheng Zhong. 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 show that a local minimizer of in the topology must be a local minimizer in the topology, under suitable assumptions for the functional with supercritical exponent . This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution. Hence, we extend the conclusion proved by Brezis and Nirenberg (1993), the subcritical and critical case.