中文摘要：

该文讨论以下带有位势V的薛定谔-泊松（Schrodinger-Poisson）系统{-△u＋λVu＋φu=f（x,u）,x∈R^3,-△φ=u-2,x∈R^3,其中λ≥1是一个参数,位势函数V∈C（R^3,R＋）满足比较一般的假设.当非线性项f在无穷远点是超四次的,并且空间嵌入缺乏紧性时,该文讨论了参数λ≥1充分大时问题解的存在性与多解性.也考虑了非线性性项f满足一般的次线性假设时问题无穷多个解的存在性.

英文摘要：

In this paper, we discuss the existence and multiplicity solutions to tke following Schrodinger-Poisson system with potentials {-△u＋λVu＋φu=f（x,u）,x∈R^3,-△φ=u-2,x∈R^3 where λ≥ 1 is a parameter, the potential V ∈ C（R^3,R＋） and satisfies the more general assumptions. When f is 4-superlinear at infinity, we discuss the existence and multiplicity of solutions for λ≥1 large enough without the compactness of embedding of the work space. We also consider the existence of infinity many solutions with f satisfying the more general sublinear assumptions.