Existence And Concentration Of Solutions Of A Class Of Nonlinear Schr(?)dinger Equations With Multi-well Potentials

This dissertation deals with a class of nonlinear Schrodinger equation as fol-lowingwhere V(x)is the external potential that has the form V(x)?e(-a|x|)?i=1n(|x-xi|+1)pi(0<?<2),K(x)denotes the interaction between the particles and has the form K(x)-e(-?|x|)?i=1n(|x-xi|+1)qi(?>0).Under the assumption?<p<(N+2)/(N-2),we prove that the equation has at least one solution u? belonging to W1,2(RN).Furthermore,we show that as ??0,u? will concentrate at a global minimum point of A=V?K-2/p-1,where ?=p+1/p-1-N/2.