Existence Of Solutions For Schr?dinger-Poisson Systems

This thesis for Master's degree considers existences of nontrivial solutions for the general Schr?dinger-Poisson systems by using the mountain pass theorem the concentration compactness argument and the dual approach.In this paper,the contents are organized as follows:In Chapter one is an introduction.we sketch the historical background,status,the up-to-date progress for the discussed problems,and some preliminaries of theorems which will be used in the next chapters.In Chapter two,we study the existences of nontrivial solutions for the periodic and asymptotically Schr?dingcr-Poisson systems with critical exponent,where V,K,f are continuous functions.In this chapter,we assume that V and K can be controlled by the periodic function of the small perturbation.By restricting the natural constraint in the radial function,this system is solved by using the concentration compactness argument combined with mountain pass theorem to deal with system.In Chapter third,by using dual approach and genus theorem,we study the existence of infinitely solutions for the Schr?dinger-Poisson system with sign-changing potential,where k is positive continuous functions,and we not require any growth condition on the nonlinear term.