Abstract In this paper we study the existence and multiplicity of positive solutions for the Schrodinger-Poisson system with critical growth: { − e 2 Δ u + V ( x ) u = f ( u ) + | u | 3 u ϕ , x ∈ R 3 , − e 2 Δ ϕ = | u | 5 , x ∈ R 3 , u ∈ H 1 ( R 3 ) , u ( x ) > 0 , x ∈ R 3 , where e > 0 is a parameter, V : R 3 → R is a continuous function and f : R → R is a C 1 function. Under a global condition for V we prove that the above problem has a ground state solution and relate the number of positive solutions with the topology of the set where V attains its minimum, by using variational methods.

中文翻译：

---

某些具有临界增长的薛定谔-泊松系统的存在性和多重性结果

摘要 本文研究了具有临界增长的薛定谔-泊松系统正解的存在性和多重性：{ − e 2 Δ u + V ( x ) u = f ( u ) + | 你| 3 u ϕ , x ∈ R 3 , − e 2 Δ ϕ = | 你| 5 , x ∈ R 3 , u ∈ H 1 ( R 3 ) , u ( x ) > 0 , x ∈ R 3 ，其中e > 0 是参数，V : R 3 → R 是连续函数，f : R → R 是 C 1 函数。在 V 的全局条件下，我们证明了上述问题具有基态解，并通过使用变分方法将正解的数量与 V 达到其最小值的集合的拓扑相关联。