Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2005, Issue 2, Pages 185-205
http://dx.doi.org/10.1155/AAA.2005.185

Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains

Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku, Tokyo 169-8555, Japan

Received 17 May 2003

Copyright © 2005 Hindawi Publishing Corporation. 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 are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains Ω:ε2Δu+a()u=u|u|p2 in Ω, u>0 in Ω, u=0 on Ω. The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the profile of a() from the variational point of view. It is shown that if a has a “peak” in Ω, then (P) has at least three solutions for sufficiently small ε.