Nodal Solutions For The Schrodinger Poisson Type Equations In R^3

In this paper,we consider the existence of nodal solutions for a Schr?dinger-Poisson-type problemBy variational method,for each k ? N+,we show that the problem(P)possesses a nodal solution changing sign exactly k times.This thesis is divided into two chapters.In chapter 1,we introduce the background of the problem,associated knowledge and main results of the thesis.In chapter 2,we consider the nodal solutions for the Schr?dinger Poisson type equations in R~3where a,b are a positive constants,p ?(2,6),u ? H1(R~3),V(x)is a smooth function and ?:R~3 ?R are unknown functions,(a + b(?)R~3 |?u|~2 dx)? is nonlocal operator.For each k ? N+,we show that the problem(P)possesses a nodal solution changing sign exactly k times.