MULTIPLE POSITIVE SOLUTIONS FOR A SINGULARLY PERTURBED DIRICHLET PROBLEM IN “GEOMETRICALLY TRIVIAL ” DOMAINS

Abstract. In this paper we consider the singularly perturbed Dirichlet problem (Pε), when the potential aε(x), as ε goes to 0, is concentrating round a point x0 ∈ Ω. Under suitable growth assumptions on f, we prove that (Pε) has at least three distinct solutions whatever Ω is and that at least one solution is not a one-peak solution