A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential

We study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of (-Δ,H01(Z)). Our approach is variational and is based on the nonsmooth critical point theory for locally Lipschitz functions. We prove the existence of at least two nontrivial solutions.