Abstract and Applied Analysis
Volume 2005 (2005), Issue 2, Pages 185-205
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 Michinori Ishiwata. 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.
We are concerned with the multiplicity of solutions of the
following singularly perturbed semilinear elliptic equations
in bounded domains in , in , on . The main purpose of this
paper is to discuss the relationship between the multiplicity of
solutions and the profile of from the variational point
of view. It is shown that if has a “peak” in , then (P) has at least three solutions for sufficiently small .