Existence Of Positive Solutions For A Class Of Quasilinear Schr(o|¨)dinger Equation

In this paper, we study existence of positive solutions for the following quasilinear Schrodinger equation Firstly, we use a change of variables to convert this quasilinear equation into a semilin-ear equation, then study the autonomous case and nonautonomous case of the above problem. In the case of nonlinearity is f(u), by using L.Jeanjean’s Theorem, we prove the boundedness of the (PS) sequence and the existence of the nontrivial solution.In the case of nonlinearity is f(x, u), by using the mountain pass theorem, we prove the existence of solutions, then construct a new path to prove nontriviality of this solution in H1(RN).