Parametric nonlinear resonant Robin problems

Abstract

We consider a nonlinear Robin problem driven by the ▫$p$▫-Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly ▫$(p-1)$▫-sublinear and the other one is ▫$(p-1)$▫-linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all big values of the parameter ▫$lambda$▫ the problem has at least five nontrivial smooth solutions