Positive and nodal solutions for parametric nonlinear Robin problems with indefinite potential

Abstract

We consider a parametric nonlinear Robin problem driven by the p-Laplacian plus an indefinite potential and a Carathéodory reaction which is (p-1)- superlinear without satisfying the Ambrosetti - Rabinowitz condition. We prove a bifurcation-type result describing the dependence of the set of positive solutions on the parameter. We also prove the existence of nodal solutions. Our proofs use tools from critical point theory, Morse theory and suitable truncation techniques.