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 −Δu=f(x,u)+λg(x,u), where Δ is the Laplacian operator, λ is a real parameter and , 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.