On Resonant Robin Problems with General Potential

Abstract

We consider a semilinear Robin problem with indefinite and unbounded potential and a reaction term which asymptotically at $$\pm \,\infty $$ is resonant with respect to any nonprincipal, nonnegative eigenvalue of the differential operator. Using critical point theory, Morse theory (critical groups) and the reduction method, we show that the problem has at least three nontrivial solutions.