Multiplicity of positive solutions for the fractional Schrödinger–Poisson system with critical nonlocal term

This paper deals with the following fractional Schrödinger–Poisson system: [Formula: see text] with multiple competing potentials and a critical nonlocal term, where [Formula: see text], [Formula: see text] or [Formula: see text], and [Formula: see text] is the fractional critical exponent. By combining the Nehari manifold analysis and the Ljusternik–Schnirelmann category theory, we establish how the coefficient [Formula: see text] of the nonlocal critical nonlinearity affects the number of positive solutions. We propose a new relation between the number of positive solutions and the category of the global maximal set of [Formula: see text].