Fractional magnetic Schrödinger equations with potential vanishing at infinity and supercritical exponents

Abstract

This paper focuses on the following class of fractional magnetic Schrödinger equations: where is the fractional magnetic Laplacian, is the magnetic potential, , N>2s, is a parameter, is a potential function that may decay to zero at infinity and is a continuous function with subcritical growth. We deal with supercritical case . Our approach is based on variational methods combined with penalization technique and -estimates.