Concentrating Solutions for Fractional Schrödinger–Poisson Systems with Critical Growth

In this paper, we consider a class of fractional Schrödinger–Poisson systems (Formula presented.) and (Formula presented.) in (Formula presented.), where (Formula presented.) with (Formula presented.), (Formula presented.) denotes a parameter, (Formula presented.) admits a potential well (Formula presented.) and (Formula presented.) is the fractional Sobolev critical exponent. Given some reasonable assumptions as to the potential V and the nonlinearity f, with the help of a constrained manifold argument, we conclude the existence of positive ground state solutions for some sufficiently large (Formula presented.). Upon relaxing the restrictions on V and f, we utilize the minimax technique to show that the system has a positive mountain-pass type by introducing some analytic tricks. Moreover, we investigate the asymptotical behavior of the obtained solutions when (Formula presented.).