Nonlinear Dirichlet Problems with no Growth Restriction on the Reaction

Abstract

We consider nonlinear Dirichlet problems driven by the sum of a $p$-Laplacian and a Laplacian and with a Carathéodory reaction which does not satisfy any global growth condition. Instead we assume that it has constant sign $z$-dependent zeros. Using variational methods, truncation techniques and Morse theory, we prove multiplicity theorems providing sign information for all the solutions.