Multiplicity of solutions for resonant Neumann problems with an indefinite and unbounded potential

Abstract

We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Carathéodory function which exhibits linear growth near ± ∞ \pm \infty . We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (the Lyapunov-Schmidt method).