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28 April 2005 Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains
Michinori Ishiwata
Abstr. Appl. Anal. 2005(2): 185-205 (28 April 2005). DOI: 10.1155/AAA.2005.185

Abstract

We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains Ω:ɛ2Δu+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 ɛ.

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Michinori Ishiwata. "Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains." Abstr. Appl. Anal. 2005 (2) 185 - 205, 28 April 2005. https://doi.org/10.1155/AAA.2005.185

Information

Published: 28 April 2005
First available in Project Euclid: 17 May 2005

zbMATH: 1128.35043
MathSciNet: MR2179442
Digital Object Identifier: 10.1155/AAA.2005.185

Rights: Copyright © 2005 Hindawi

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