The Ground State Solution Of A Nonlinear Schr(?)dinger Equation With Variable Coefficients

In this thesis,we investigate the following nonlinear Schrodinger system with variable coefficients defined on RN(N=2,3)(?)where 0<?<<1 is a small parameter.This system arises from the study of the Bose-Einstein condensates.We consider two kinds of external potentials denoted by Vj(x)(j=1,2):1)Vj(x)?+? as |x|?+?;2)Vj(x)<+?.Under some proper assumptions,by virtue of the compact embedding of the weighted Sobolev space and the concentration-compactness principle,we obtain the existence of ground state solutions under the two kinds of external potentials respectively.