On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases

In this paper, we establish the existence of standing wave solutions for a class of nonlinear fractional Schrödinger-Poisson system involving nonlinearity with subcritical and critical growth. We suppose that the potential V satisfies either Palais-Smale type condition or there exists a bounded domain \(\varOmega \) such that V has no critical point in \(\partial \varOmega \). To overcome the “lack of compactness" of the problem, we combine Del Pino-Felmer’s penalization technique with Moser’s iteration method and some ideas from Alves [1].