Singular and Superlinear Perturbations of the Eigenvalue Problem for the Dirichlet p-Laplacian

We consider a nonlinear Dirichlet problem, driven by the p-Laplacian with a reaction involving two parameters lambda is an element of R, theta > 0. We view the problem as a perturbation of the classical eigenvalue problem for the Dirichlet problem. The perturbation consists of a parametric singular term and of a superlinear term. We prove a nonexistence and a multiplicity results in terms of the principal eigenvalue (lambda) over cap (1) > 0 of (-Delta(p), W-0(1,p)(Omega)). So, we show that if lambda >= (lambda) over cap (1) and theta > 0, then the problem has no positive solution, while if lambda < <(lambda)over cap>(1) and theta > 0 is suitably small (depending on lambda), there are two positive smooth solutions.