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| In this paper, we investigate the following Chern-Simons-Schr\"{o}dinger system\begin{equation*}\label{css}\begin{cases} -\Delta u+ u+A_{0}u+A_{1}^{2}u+A_{2}^{2}u=f(u), \\ \partial_{1}A_{2}-\partial_{2}A_{1}=-\frac{1}{2}u^{2},\qquad\partial_{1}A_{1}+\partial_{2}A_{2}=0,\\ \partial_{1}A_{0}=A_{2}u^{2}, \qquad \partial_{2}A_{0}=-A_{1}u^{2},\end{cases}\end{equation*}where $\partial_{1}=\frac{\partial}{\partial x_{1}}, \partial_{2}=\frac{\partial}{\partial x_{2}}$ for $x=\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}$, $A_{j} : \mathbb{R}^{2} \rightarrow \mathbb{R}$ is the gauge field $(j=0,1,2)$. If $f$ satisfies the suitable subcritical conditions.By using variational methods, we prove that Chern-Simons-Schr\"{o}dinger system has infinitely many high energy radial solutions. |
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| Keywords:Chern-Simons-Schr\"{o}dinger system; High energy radial solutions; Trudinger-Moser inequality; Symmetric mountain pass; Minimax principle |
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