Existence of solutions for a perturbed Dirichlet problem without growth conditions

Abstract

We present some results on the existence and multiplicity of solutions for boundary value problems involving equations of the type − Δ u = f ( x , u ) + λ g ( x , u ) , where Δ is the Laplacian operator, λ is a real parameter and f , g : Ω × R → R , Ω ⊂ R N are two Carathéodory functions having no growth conditions with respect to the second variable. The approach is variational and mainly based on a critical point theorem by B. Ricceri.