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In this paper, we study the existence of multiple positive solutions for aclass of fractional Schr\"{o}dinger-Poisson systems involving sign-changingpotential and critical nonlinearities on an unbounded domain. With the help ofNehari manifold and Ljusternik-Schnirelmann category, we investigate how thecoefficient $g(x)$ of the critical nonlinearity affects the number of positivesolutions. Moreover, we present a novel relationship between the number ofpositive solutions and the category of the global maximum set of $g(x)$.

Multiple positive solutions for the fractional Schr\"{o}dinger-Poisson systems involving critical nonlinearities with potential