We are concerned with the nonlinear Schrödinger-Poisson equation

$$\begin{cases}-\Delta u+(V(x)-\lambda)u+\phi(x)u=f(u),\\-\Delta\phi=u^{2},\lim\limits_{\vert x\vert\rightarrow+\infty}\phi(x)=0,x\in \mathbb{R}^{3},\end{cases}\ {\mathrm{(P)}}$$

where λ is a parameter, V (x) is an unbounded potential and f (u) is a general nonlinearity. We prove the existence of a ground state solution and multiple solutions to problem (P).

中文翻译：

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具有一般非线性的Schrödinger-Poisson方程的多重解

我们关注非线性Schrödinger-Poisson方程

$$ \ begin {cases]-\ Delta u +（V（x）-\ lambda）u + \ phi（x）u = f（u），\\-\ Delta \ phi = u ^ {2}，\ lim \ limit _ {\ vert x \ vert \ rightarrow + \ infty} \ phi（x）= 0，x \ in \ mathbb {R} ^ {3}，\ end {cases} \ {\ mathrm {（P）}} $$

其中λ是参数，V（x）是无穷大的电势，f（u）是一般的非线性。我们证明了存在基态解决方案和问题（P）的多种解决方案。