Existence results for a fractional Schrödinger–Poisson equation with concave–convex nonlinearity in ℝ3

In this paper, we consider the following nonhomogeneous fractional Schrödinger–Poisson equations: where λ ≥ 0, s ∈ (3/4, 1], t ∈ (0, 1], (− Δ) s denotes the fractional Laplacian. g ( x , u ) is of general 3‐superlinear growth at infinity, f ( x , u ) satisfies sublinear growth conditions. By means of some critical point theorems, we obtain the following results: (1) the existence of at least one solution for , (2) the existence of at least two nontrivial solutions for λ > 0 small enough, (3) the infinitely many solutions when f ( x , u ) is odd in u and λ > 0.