Semilinear neumann equations with indefinite and unbounded potential

Abstract

We consider a semilinear Neumann problem with an indefinite and unbounded potential, and a Carathéodory reaction term. Under asymptotic conditions on the reaction which make the energy functional coercive, we prove multiplicity theorems producing three or four solutions with sign information on them. Our approach combines variational methods based on the critical point theory with suitable perturbation and truncation techniques, and with Morse theory.