Schrödinger p⋅–Laplace equations in RN involving indefinite weights and critical growth

Abstract

We study a class of critical Schrödinger p⋅–Laplace equations in RN, with reaction terms of the concave–convex type and involving indefinite weights. The class of potentials used in this study is different from that in most existing studies on Schrödinger equations in RN. We establish a concentration-compactness principle for weighted Sobolev spaces with variable exponents involving the potentials. By employing this concentration-compactness principle and the Nehari manifold method, we obtain existence and multiplicity results for the solution to our problem.