拟线性薛定谔方程源于数学物理中的多种模型，其驻波解备受关注。本项目利用临界点理论的相关工具结合分析技巧，研究拟线性薛定谔方程的非平凡的驻波解的存在性和多重性。具体内容包括：(1)利用Pohozaev流形，集中紧性原理以及截断技巧，Moser迭代等分析手段，研究次临界或临界的Berestycki-Lions条件下拟线性薛定谔方程的基态解的存在性。(2)利用广义Nehari流形，广义弱环绕等工具研究强不定情形下拟线性薛定谔方程驻波解的存在性和多重性。(3)利用各种不等式以及广义山路引理，集中紧性原理，研究带Hardy项和双临界指数的拟线性薛定谔方程驻波解的存在性和多重性。通过本项目的实施，不仅可以使得拟线性薛定谔方程具有更广泛的适用性，而且有助于一些数学理论分支的发展。

Quasilinear Schrodinger equation originates from many models in mathematical physics, and its standing wave solution attracts much attention. In this project, the existence and multiplicity of non-trivial standing wave solutions for the Quasilinear Schrodinger equations are studied by means of critical point theory and analytical techniques.The following contents are included: (1)The existence of ground state solutions for Quasilinear Schrodinger equation with subcritical or critical Berestycki-Lions conditions are studied by means of Pohozaev manifold, centralized compactness principle, truncation technique and Moser iteration. (2)The existence and multiplicity of standing wave solutions for strongly indeterminate Schrodinger equation are studied by means of generalized Nehari manifold and generalized weak surroundings. (3)The existence and multiplicity of standing wave solutions for Quasilinear Schrodinger equation with Hardy term and double critical exponents are studied by using various inequalities, generalized mountain pass lemma and concentration compactness principle. Through the implementation of this project, it not only makes the quasilinear Schrödinger equation more widely used, but also contributes to the development of some branches in mathematical.