Research announcement Resonant Neumann problems with indefinite and unbounded potential

a b s t r a c t 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 Caratheodory 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.