The Existence Of Nodal Solutions Of Nonlinear Choquard Equations

In this thesis,we investigate the existence of nodal solutions of the nonlinear Choquard equation(P),where 5/2<P<5.We intend to show that for every fixed integer k,there exists a pair radial solutions of problem(P)which change sign exactly k times.This thesis is divided into three chapters.In chapter 1,we introduce the background of the problem and main results of the thesis.In chapter 2,we present variational framework to deal with problem(P)and find a minimizer of the related minimization problem.In chapter 3,for any positive integer k,we prove that the system (Pi) has a least energy solution.Then,we glue the first-order derivative of the least energy solution of problem(Pi)at each node to obtain a pair radial solutions of the nonlinear Choquard equation(P),which change sign exactly k-times.