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 Ω such that V has no critical point in ∂ Ω . 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]. [ABSTRACT FROM AUTHOR]