In this paper, simulated by the paper of Wei and Yan [33] (see also [30–32]), we intend to find infinitely many positive solutions to (1.2) for all p ∈ (1, 5) under weaker integrability conditions on K(y) and Q(y). In [33], a single equation, this is, K(y) ≡ 0 in (1.2), was studied and infinitely many non-radial solutions were found in the case that Q(y) is radial. For this, they employed a very novel idea, that is, they use k, the number of the bumps of the solutions, as the parameter to construct Infinitely Many Solutions for Schrödinger-Poisson System 1071 spike solutions for the Schrödinger equation considered.