Existence results for nonhomogeneous fractional Schrödinger-Poisson systems involving critical exponents

In this paper, we investigate a class of nonhomogeneous fractional Schrödinger-Poisson systems with subcritical or critical nonlocal term, and a nonlinearity involving critical and subcritical growth. Meanwhile, we assume that the potential function can change sign, which is also a novelty of our results. By using a fixed point theorem, we can find a nontrivial weak solution in a reflexive Banach semilattice. Furthermore, in the last part of the article, we apply the fixed point theorem to handle a class of Schrödinger-Poisson systems with inconsistent fractional exponents and obtain an existence result.