近年来，非线性问题在固体物理、核物理、化学等领域中有越来越广泛的应用，研究者们不断地对此类问题进行研究，并建立了很多重要的理论方法来解决此类问题，其中变分方法是解决此类问题的一个有效工具。Schrodinger 方程是量子力学中的一个基本方程，在物理学中有着非常广泛的应用，许多学者对其解的存在性及性质进行了研究，并使用了很多性质有效的研究方法，如变量代换方法、Nehari 流形方法、正则化方法等等。 考虑如下临界拟线性 Schrodinger 方程 -\Delta u+V_{\lambda}(x)u-u\Delta(u^{2})=P(x)|u|^{p-1}u+Q(x)|u|^{22^{*}-2}u,\quad u>0,~x\in\mathbb{R}^{N}， 本文将研究该方程正的基态解的存在性及其渐近行为。 在第一章中，主要介绍了本文的研究背景和现状, 并给出本文的主要结果。 在第二章中，介绍了一些与本文相关的基本定义和基本定理。 在第三章中，首先通过变量代换方法，将拟线性 Schrodinger 方程转化为半线性 Schrodinger 方程，然后研究该半线性 Schrodinger 方程的能量泛函，通过其山路结构，几个能量值的比较及极限能量泛函的一些估计来确定原能量泛函最小能量值的可达性，从而得出方程的基态解的存在性。 在第四章中，在有界区域上进行考虑，可以得到类似第三章的结论，得出在有界区域上对应的 Drichlet 问题的基态解的存在性，然后令~$\lambda\rightarrow\infty$，得出极限情形下该方程的基态解与相应的有界区域上的 Drichlet 问题的解之间的渐近关系。

In recent years, nonlinear problems have more and more application in the field of solid state physics, nuclear physics, chemistry, etc. Researchers constantly put into study on such problems, and they have set up a number of important theoretical methods to solve such problems. Variational method is an effective tool to solve these problems. Schrodinger equations are fundamental equations in quantum mechanics, which are widely used in physics. Many scholars have studied the existence and properties of their solutions and used many effective research methods, such as the variable substitution method, the Nehari manifold method, the regularization method and so on. Consider such critical quasilinear Schrodinger equation -\Delta u+V_{\lambda}(x)u-u\Delta(u^{2})=P(x)|u|^{p-1}u+Q(x)|u|^{22^{*}-2}u,\quad u>0,~x\in\mathbb{R}^{N}, In this paper, we aim to study the existence of positive ground state solutions and their concentration behavior. In the first chapter, we mainly introduce the research background and status of this problem, and give the main results of this paper. In the second chapter, we list some basic definitions and theorems. In the third chapter, using the variable substitution method, we transform the quasilinear Schrodinger equation into a semilinear Schrodinger equation, and then study the energy functional of the semilinear Schrodinger equation. By the mountain pass geometry, comparison of several energy values and some estimates of the limit functional, we determine the reachability of the least energy value of the primary energy functional, and thus it is concluded that the ground state solutions of the equation exist. In the fourth chapter, taking a bounded region into consideration, we get similar conclusions with the third chapter, so we prove the existence of the ground state solutions of the corresponding Drichlet problem. Then, by taking $\lambda \rightarrow\infty$, the asymptotic relationship in the limit conditions between the ground state solutions of this equation and the solution of the corresponding Drichlet problem in the bounded region can be obtained.