In this paper, we study the following modified quasilinear Schrödinger equation $\begin{array}{rl}& -\mathrm{\Delta }u+V\left(x\right)u-\kappa u\mathrm{\Delta }\left(u^2\right)+q\frac{h^2\left(|x|\right)}{|x{|}^2}(1+\kappa u^2)u\\ & +q\left({\int }_{|x|}^{+\mathrm{\infty }}\frac{h\left(s\right)}{s}(2+\kappa u^2(s\left)\right)u^2\left(s\right)\mathrm{d}s\right)u=|u{|}^{p-2}u\mathrm{i}\mathrm{n}{\mathbb{R}}^2,\end{array}$ where $\kappa >0$, q>0, p>6 and $V\in \mathcal{C}({\mathbb{R}}^2,\mathbb{R})$. We develop a more direct and simpler approach to prove the existence of ground state solutions. Our method is based on the Poho$\check{z}$aev type identity and monotone trick.

中文翻译：

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修正的拟线性薛定谔方程与陈-西蒙斯规范理论耦合的基态解

在本文中，我们研究了以下修正的拟线性薛定谔方程$\begin{array}{rl}& -\mathrm{\Delta }你+五\left(X\right)你-\kappa 你\mathrm{\Delta }\left({你}^2\right)+q\frac{H^2\left(|X|\right)}{|X{|}^2}(1+\kappa {你}^2)你\\ & +q\left({\int }_{|X|}^{+\mathrm{\infty }}\frac{H\left(s\right)}{s}(2+\kappa {你}^2(s\left)\right){你}^2\left(s\right)\mathrm{d}s\right)你=|你{|}^{p-2}你\mathrm{一世}\mathrm{n}{\mathbb{R}}^2,\end{array}$在哪里$\kappa >0$, q >0, p >6 和$五\in \mathcal{C}({\mathbb{R}}^2,\mathbb{R})$. 我们开发了一种更直接和更简单的方法来证明基态解决方案的存在。我们的方法基于 Poho$\check{z}$aev 类型标识和单调技巧。