This paper is focused on the following Schrödinger–Poisson system −Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, where V(x) is weakly differentiable and tends asymptotically to a constant and f∈C(R,R). By introducing some new tricks, we prove that the above system admits a ground state solution under somemild assumptions on V and f. Our results generalize and improve the existing ones in the literature.

中文翻译：

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渐近恒定势的薛定ding-泊松系统的基态解

本文着重于以下Schrödinger-Poisson系统-Δu+ V（x）u + ϕu = f（u），x∈R3，-Δϕ = u2，x∈R3，其中V（x）是微分可微的并且趋向于渐近为常数和f∈C（R，R）。通过引入一些新的技巧，我们证明上述系统在V和f的一些假定条件下可以接受基态解。我们的研究结果概括并完善了文献中已有的研究结果。