Stability And Instability Of Standing Waves For Nonlinear Choquard Equation

The author introduces the main results obtained during the period he applied for the master degree in this article.In this dissertation,the nonlinear Choquard equation with deep physical background is studied.For instance,it is known to describe the propagation of electromagnetic waves in plasmas and plays an important role in the theory of Bose-Einstein condensation.This equation,which is also called the Hartree equation or the Schrodinger-Newton equation,has attracted a great deal of attention in theoretical over the past years.In the Chapter 2 and Chapter 3,the author introduces the instability and stability of standing waves for nonlinear Choquard equation.In chapter 2,the author considers the following generalized Choquard equation with potential,(?)(?)(?)When 2 +(2-?)/3<p<6-?,the author learns to the blow up solution of equation in finite time to obtain the instability of the standing waves.In chapter 3,the author studies the equation with 2<p<2 + ?,(?)(?)(?)There exists ?>0.When V(x)satisfies some conditions,we can prove the stability of standing waves.