POSITIVE SOLUTIONS OF FRACTIONAL SCHRODINGER-POISSON SYSTEMS INVOLVING CRITICAL NONLINEARITIES WITH POTENTIAL

In this paper, we study the existence of multiple positive solutions for a class of fractional Schrodinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. By means of the Nehari manifold and Ljusternik-Schnirelmann category, we show how the coefficient g(x) of the critical nonlinearity affects the number of positive solutions, and present a novel relationship between the number of positive solutions and the category of the global maximum set of g(x). The new feature which distinguishes this paper from other related works lies in the fact that we focus on the case of 1 < q < 2, which has not been presented in the literature.