Existence of solutions for a perturbed Dirichlet problem without growth conditions

We present some results on the existence and multiplicity of solutions for boundary value problems involving equations of the type − u = f (x,u) + λg(x, u), where is the Laplacian operator, λ is a real parameter and f, g :Ω × R→R, Ω ⊂ RN 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. © 2006 Elsevier Inc. All rights reserved.