具有临界指数增长的广义 Chern-Simons-Schrödinger 系统：零质量情形
Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case
AI总结：
本文研究零质量 Chern-Simons-Schrödinger 系统在 Trudinger-Moser 临界指数增长下基态解的存在性，通过改进 Trudinger-Moser 不等式并运用变分法证明了正基态解的存在。
摘要：
我们考虑一类零质量 Chern-Simons-Schrödinger 系统基态解的存在性，其中 $a:\mathbb R^2\to\mathbb R^+$ 为外部势，$p\in(1,2)$，$f\in \mathcal{C}(\mathbb R)$ 表示在无穷远处满足 Trudinger-Moser 意义下临界指数增长的非线性项。通过引入 Trudinger-Moser 不等式版本的改进，我们能够利用变分法研究该系统正基态解的存在性。
英文摘要：
We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schrödinger systems \[ \left\{ \begin{array}{ll} \displaystyle -Δu +A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \newline \displaystyle \partial_1A_2-\partial_2A_1=-\frac{1}{2}|u|^2,~\partial_1A_1+\partial_2A_2=0, \newline \displaystyle \partial_1A_0=A_2|u|^2,~ \partial_2A_0=-A_1|u|^2, \end{array} \right. \] where $a:\mathbb R^2\to\mathbb R^+$ is an external potential, $p\in(1,2)$ and $f\in \mathcal{C}(\mathbb R)$ denotes a nonlinearity that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. By introducing an improvement of the version of Trudinger-Moser inequality, we are able to investigate the existence of positive ground state solutions for the given system using variational method.
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