The Existence Of Solutions For Quasilinear Schr(?)dinger Equations

This paper discusses the existence result of positive solutions for a quasilinear Schrodi-nger equations, Quasilinear Schrodinger equations are one of the most active research topics and are a basic quantum mechanics equation, it has been widely applied to various fields, making use of some conventional theory tools such as Mountain pass lemma, Trans-formation theory and Critical point theory, we focuse mainly on the existence of solutions for some quasilinear Schrodinger equations:Firstly, the existence of Soliton solutions for quasilinear Schrodinger equations; Secondly, Quasilinear Schrodinger equations involving critical exponents in R2.The first chapter is an introduction. The research background and preliminary knowl-edge of the problem are briefly introduced, and state the main research contents of this paper.The second chapter is concerned with the existence result of positive solutions for a quasilinear elliptic equation arising from plasma physics. This converts a quasilinear elliptic equation into a semilinear one and use Cerami condition and the Mountain pass theorem, we show the existence result for this quasilinear Schrodinger equation under the suitable conditions on the power of nonlinearity and quasilinearity.The third chapter studys the existence of soliton solutions for a class of Quasilinear Schrodinger equations in R2with critical exponential growth. This use mainly Mountain pass lemma, Trudinger-Moser inequality and Critical point theory Etc.