Existence of positive solutions to the Schrödinger–Poisson system without compactness conditions

In this paper, we discuss the existence of a positive radial solution to a generalized Schrödinger–Poisson system without compactness conditions. By the method of the combination of a cut-off function, a monotonicity trick and a Pohozaev type identity, we obtain the boundedness of a Palais–Smale sequence.