Multiplicity results for a boundary value problem with Dirichlet condition

Abstract

In this note, the existence of at least three weak solutions for the � −div(|∇u|∇u )+ λf (x, u )= −a(x)|u|u in Ω, u =0 on ∂Ω, where Ω ⊂ R 2 is non-empty bounded open set with smooth boundary ∂Ω, λ> 0, f :Ω × R → R is a coninuous function and and positive weight function a(x) ∈ C(Ω), is established. The approach is based on variational methods and critical points.