The Existence Of Solutions For A Class Of Nonlinear Schr(?)dinger Equation

In this paper, we study existence of positive solutions for the following quasilinear Schrodinger equation The value of diffusion parameter k is different,which means the equation has a different meaning.For k< 0,we use a change of variables to convert this quasilinear equation into a semilinear equation, then we study the conditions of equation and the properties of this function, we proved the conditions of mountain geometric.Finally,by using the Mountain-Pass theorem, we proved the existence of nontrivial solutions for this equation. In the case k<0,we use variational methods combined with perturbation arguments to convert this quasilinear equation into a semilinear equation,however, variable transformation function is piecewise form,therefore,after we prove the existence of nontrivial solutions for this equation by using the Mountain-Pass theorem,we need prove this solutions under proper ranges of,this is,||L∞||∞ is bounded.