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(R^N). For a local minimum x<inf>0</inf> of the potential V(x), we show that there exists a sequence ε<inf>n</inf> → 0, for which corresponding solutions u<inf>n</inf>(x) ∈ H ¹(R^N) concentrate at x<inf>0</inf>. Our assumptions on f(ε) are mainly the ones under which the associated autonomous problem -Δv + V(x<inf>o</inf>)v = f(v), v ∈ H¹(R^N), admits a non trivial solution.

Año de publicación:

2005

Keywords:

• Singularly perturbed elliptic problems
• Variational methods

Fuente:

scopus