薛定谔泊松系统的无穷多高能量解

In this arcitle, we investigate the following Schr\"{o}dinger-Poisson system\begin{equation*} \begin{cases} -\Delta u+V(x)u+\phi u=f(u), & \text{ in }\R,\\ -\Delta \phi= u^2, & \text{ in }\R, \end{cases}\end{equation*}where $V(x)$ is coercive, $f$ satisfies that $\frac{1}{3}f(t)t\geq F(t)>0$ for every $t\in\RRR\setminus\{0\}$. Under certain assumptions about the above terms, we obtain infinitely many high energy solutions for the system by Symmetric mountain pass theorem.