Multiple Pertubations To A Quasilinear Schrodinger Equation

This paper is concerned with a more general class of quasilinear equa-tions than the standard Schrodinger equation(?)=-h2/2m??+V?,which consists of a class of the initial value problem of nonlinear equations with potential term,Hartree term and multiple nonlinear terms in N dimensional Euclidean space.we obtain finally the sufficient condition of the global exis-tence and blow up in finite time of the solution of the quasilinear Schrodinger equation.In summary,this paper extends some results in the literature to the quasilinear case which bears more general physical models.The Cauchy problem isThis thesis contains five chapters.The first one is the introduction,which introduces the research background,research status and important in-equalities of the Schrodinger equation.Chapter 2 is the preliminaries,which discusses the researched problem,definitions and main results.We also give some important lemmas here,which will be used frequently in the subse-quent proof.In the next two chapters,we will respectively explore and prove the sufficient condition of the global existence and blow up in finite time of the solution of the quasilinear Schrodinger equation.The fifth chapter is the conclusion,which proposes that we can continue to explore to obtain a sharp threshold for global existence and blow up for the solution,and some general proof steps will be given here.