Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains

Michinori Ishiwata

Abstract and Applied Analysis, 2005, vol. 2005, 1-21

Abstract:

We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains Ω : − ε 2 Δ u + 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:702781

DOI: 10.1155/AAA.2005.185

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