Abstract
We consider the following singularly perturbed elliptic problemε2Δu˜−u˜+u˜p=0,u˜>0inΩ,∂u˜∂n=0on∂Ω, where Ω is a bounded domain in R3 with smooth boundary, ε>0 is a small parameter, n denotes the inward normal of ∂Ω and the exponent p>1. Let Γ be a hypersurface intersecting ∂Ω at the right angle along its boundary ∂Γ and satisfying a non-degeneracy condition. We establish the existence of a solution uε concentrating along a surface Γ˜ close to Γ, exponentially small in ε at any positive distance from the surface Γ˜, provided ε is small and away from certain critical numbers. The concentrating surface Γ˜ will collapse to Γ as ε→0.
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