Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains

Michinori Ishiwata

Abstract and Applied Analysis, 2005, vol. 2005, issue 2, 185-205

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|p−2 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.

Date: 2005
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https://doi.org/10.1155/AAA.2005.185

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2005:y:2005:i:2:p:185-205

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