Existence And Asymptotic Profiles Of Solutions To Quasilinear Schr?dinger Equations

In this paper,we study the existence and asymptotic profiles of solutions of(gener-alized)quasilinear Schr?dinger equations.Firstly,we are concerned with the existence of positive solutions to the following quasilinear Schr?dinger equation which describes the nonlinear dynamics of the superfluid condensate in R~3:(?)where λ,κ,α and β are positive constants.Secondly,we study the asymptotic profiles of solutions when κ→0~+.In addition,by using the ODE method,we prove the existence of radial solutions for generalized quasilinear Schr?dinger equations.(?)where div is the divergence operator,g is a smooth even function,N≥3,p>2.