Existence Of Solutions Of Two Schrodinger Poisson Equations

With the development of science and technology, the nonlinear func-tional analysis has become one important research directions in modern mathematics both to have the profound theory and to have the widespread application. It takes the nonlinear problems appearing in mathematics and physics as background to establish some general theories and methods to handle nonlinear problem. Nonlinear differential equation problem stem-s from applied mathematics, cybernetics, physics, science in a variety of applications. It is an important kind of question in the differential equa-tions. And it is also one of most attention domains of functional analysis studies at present. So it attaches more and more attention.In this paper we first give that a Schrodinger-Poisson equation, which is involving sign-changing weight functions, has two positive solutions. The proof of this theorem relies on a few necessary lemmas. We need to use some knowledge of Nehari manifold and fibering maps during the proof, and put the equation on the Nehari manifold to obtain the properties of the solutions. Then the existence of the solutions for the usual Schrodinger-Poisson equation under the different conditions is established and proved.The thesis is divided into three sections according to contents.In chapter 1 we introduce some fundamental knowledge and source of theory.In chapter 2 we consider a class of Schrodinger-Poisson equation which is involving sign-changing weight functions and its positive solutions.In chapter 3 we consider the existence of the solutions for a class of Schrodinger-Poisson equation under the different conditions.