Fractional choquard equations with confining potential with or without subcritical perturbations

Abstract

© 2019 Walter de Gruyter GmbH, Berlin/Boston 2020. In this paper, we consider fractional Choquard equations with confining potentials. First, we show that they admit a positive ground state and infinitely many bound states. Then we prove the existence of two signed solutions when a superlinear and subcritical perturbation is added; in this case, the main feature is that such a perturbation does not satisfy the usual Ambrosetti-Rabinowitz condition.