Strong Instability Of Standing Waves For A Quasi-linear Schr（?）dinger Equation

We study a quasi-linear Schr（?）dinger equation iΦt+ΔΦ+ΦΔ（?）+（?）Φ=0.By considering the related variational problems,we prove the strong instability of standing waves for the critical case p=3+4/N.Moreover,we investigate the properties of the set of ground states,it is helpful to further study the stability of standing waves.This thesis is organized as follows:In Chapter 1,we introduce the background of the quasi-linear Schr（?）dinger equations and the related research results.In Chapter 2,we prove some basic lemmas.In Chapter 3,we introduce some results of the local well posedness of the quasi-linear Schr（?）dinger equations.In Chapter 4,we complete the proof of main results.