Abstract

AbstractWe 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 ‐sublinear and the other one is ‐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 λ the problem has at least five nontrivial smooth solutions.

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