We consider a class of Chern-Simons-Schrödinger system

$ \begin{align*} \begin{cases} -\Delta u+V(x) u+A_{0}u+\sum\limits_{j = 1}^{2} A_{j}^{2}u = g(u), \\ \partial_{1}A_{0} = A_{2}|u|^{2}, \ \ \partial_{2}A_{0} = -A_{1}|u|^{2}, \\ \partial_{1}A_{2}-\partial_{2}A_{1} = -\frac{1}{2}u^{2}, \ \ \partial_{1}A_{1}+\partial_{2}A_{2} = 0, \end{cases} \end{align*} $

中文翻译：

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具有不定势的陈-西蒙-薛定谔系统的非平凡解的存在性

我们考虑一类Chern-Simons-Schrödinger系统

$ \begin{align*} \begin{cases} -\Delta u+V(x) u+A_{0}u+\sum\limits_{j = 1}^{2} A_{j}^{2}u = g(u), \\ \partial_{1}A_{0} = A_{2}|u|^{2}, \ \ \partial_{2}A_{0} = -A_{1}|u| ^{2}, \\ \partial_{1}A_{2}-\partial_{2}A_{1} = -\frac{1}{2}u^{2}, \ \ \partial_{1}A_ {1}+\partial_{2}A_{2} = 0, \end{cases} \end{align*} $