A result on singularly perturbed elliptic problems

Abstract:

We consider a class of equations of the form -ε2Δu + V(x)u = f(u), u ∈ H1(RN). For a local minimum x0 of the potential V(x), we show that there exists a sequence εn → 0, for which corresponding solutions un(x) ∈ H 1(RN) concentrate at x0. Our assumptions on f(ε) are mainly the ones under which the associated autonomous problem -Δv + V(xo)v = f(v), v ∈ H1(RN), admits a non trivial solution.

Año de publicación:

2005

Keywords:

• Singularly perturbed elliptic problems
• Variational methods

Fuente:

scopus