First, we consider one kind of Schr(?)dinger-Poisson equations system: where u∈H1(R3),1< q< 2,λ>0, and k≠0. Assume that h(x) satisfies the following condition:In the critical growth conditions, by the Mountain Pass Theorem and variational methods, we can obtain the following result:Theorem 1 Suppose that 1<q<2,λ>0, k≠0 and (H0) holds. Then there exists λ*> 0 such that problem (SP) has at least one positive solutions (u,φu) ∈H1(R3) x D1,2(R3) for λ ∈(0,λ*).Second, we consider the other kind of Schr(?)dinger-Poisson system: where 1<q<2 and λ> 0. We will make the following assumptions on h and l:In the critical growth conditions, by the Mountain Pass Theorem, variation-al methods and concentration compactness principle, we can obtain the following result:Theorem 2 Assume 1< q< 2, the hypotheses (H1) and (H2) hold. Then there exists λ*> 0 such that problem (P) has at least two positive solutions (u,φu)∈ D1,2(R3)×D1,2(R3) for λ ∈ (0,λ*). |