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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 148902, 6 pages
http://dx.doi.org/10.1155/2014/148902
Research Article

A Concentration Phenomenon for p-Laplacian Equation

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

Received 27 April 2014; Accepted 8 July 2014; Published 20 July 2014

Academic Editor: Chao Yan

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

It is proved that if the bounded function of coefficient in the following equation   is positive in a region contained in Ω and negative outside the region, the sets shrink to a point as , and then the sequence generated by the nontrivial solution of the same equation, corresponding to , will concentrate at with respect to and certain -norms. In addition, if the sets shrink to finite points, the corresponding ground states only concentrate at one of these points. These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case .