  We consider a nonlinear, nonhomogeneous Robin problem with an indefinite
potential and a nonsmooth primitive in the reaction term. In fact, the
right-hand side of the problem (reaction term) is the Clarke subdifferential of
a locally Lipschitz integrand. We assume that asymptotically this term is
resonant with respect the principal eigenvalue (from the left). We prove the
existence of three nontrivial smooth solutions, two of constant sign and the
third nodal. We also show the existence of extremal constant sign solutions.
The tools come from nonsmooth critical point theory and from global
optimization (direct method).
