Non-radial Multipeak Positive Solutions For The Schrodinger-Possion Problem

In this paper,we consider the following Schrodinger-Poisson problem (?) where ε>0 is a small parameter,N≥3,and V(x)is a potential function.This system describes some physical phenomena such as quantum mechanics models.We construct non-radial positive solutions,whose components may have spikes clustering at the same point as ε→0+,but the distance between them divided by ε will go to infinity.This thesis is organized as follows:In chapter 1,we introduce the background of the problem and main theorem of the thesis.In chapter 2,we will give some preliminaries and make an energy expansion for the functional corresponding to Schrodinger-Poisson problem.In chapter 3,we will carry out a reduction procedure and study the reduced finite dimensional problem to prove relevant theorem.