Multiplicity results for fractional magnetic problems involving exponential growth

Abstract

The purpose of this paper is to investigate the existence and multiplicity of weak solutions for a class of nonlocal problems involving the fractional magnetic operator and nonlinearities which may have critical or subcritical growth in the sense of Trudinger-Moser inequality. By using variational methods based on minimax argument and assuming suitable conditions on the nonlinearity, we address essential geometric cases of the associated energy functional, such as the mountain pass geometry and the linking geometry. Some of the main results established in this work are new even when the magnetic potential is equal to zero, which corresponds to the usual fractional Laplacian operator.