Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains - Michinori Ishiwata (Abstract and Applied Analysis)
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.