Research Of A Class Of Quasilinear Schr?dinger Equation

In the paper, we are concerned with the existence of nontrivial solution for a class of quasilinear Schr?dinger equation which arises from plasma physics by using some mathematical theories such as mountain pass lemma, P-S condition, critical point theory,Ekeland variational principle. Through the variable transformation, the semilinear equation is converted into a quasilinear one with some relevant conditions.In the third chapter, we are concerned with the existence of nontrivial solution to the following Schr?dinger equation with A-R condition and mountain pass lemma.In the fourth chapter, without A-R condition, we study the existence of nontrivial solution to the following equation.First, we can prove the existence of the first nontrivial solution by using Ekeland variational principle; second, we can make use of mountain pass lemma, P-S condition to study the existence of the other nontrivial solution.