Resonant Neumann problems with indefinite and unbounded potential

In this paper, we report on some recent results obtained in our joint paper Papageorgiou and Rădulescu (in press). We establish multiplicity properties for a class of semilinear Neumann problems driven by the Laplacian plus on unbounded and indefinite potential. The reaction is a Carathéodory function which exhibits linear growth near ±∞. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue. The approach combines critical point theory, Morse theory and the Lyapunov-Schmidt method.