Ground State Solutions For Coupled Schr?dinger Systems And Semiclassical Solutions For Quasilinear Schrodinger Equations

In this thesis,we apply variational methods to consider Schrodinger equation(s)in different space.In Chapter 1,the author introduces the research background,development of Schrodinger equation(s)around the world,and some preliminary knowledge.In Chapter 2,the author studies the existence of solutions and other results for the coupled nonlinear Schrodinger equations on star graphs.In the establishment,we mainly use variational method to study energy functional of equations and the existence of ground states.In Chapter 3,we are interested in the semiclassical solutions and concentration results of the following quasilinear Schrodinger equation-?2?u+V(x)u-?2[?(7u2)]u=Q(x)h(u)in R2.We employ a version of the Trudinger-Moser inequality and mountain-pass arguments to get main results in a nonstandard Orlicz space.