Existence Of Fundamental Solutions For A Class Of Superlinear Schrodinger Equation

With the development of science and technology, the critical point theory began with mountain pass theory has become an important research direction in modern mathematics. A large number of scholars have achieved fruitful research results on this issue. In recent years, with the deepening of research, the research for variational prob-lem has focused on its breakthrough on content and method, and people has focused on more deep-seated problems of the solution in variational problem. For example, the research Schrodinger-poisson equations, on nonlinear Schrodinger equations and the equations of nonlinear variational problems. Many new theories and methods of the research enriches the intellectual framework of critical point theory, promoting the progress and development in the field of nonlinear functional analysis.In this paper we discuss and study some superlinear Schrodinger equation by variational methods, compared with other references, we obtain results by weakening (AR) conditions. We first prove the existence of (PS)c condition for the equation by the mountain pass lemma, then, after that we prove the existence of ground state solution for the equation. In the last part, we discuss the relations between in ground state solution and this of its "limit" equation.The thesis is divided into two sections according to contents.Chapter1Preference, we mainly introduce related knowledge and several impor-tant theorems in this research.Chapter2In this chapter, we study the superlinear Schrodinger equation Here Vλ(x)=1+λg(x), λ>0,N≥3.Under reasonable assumptions, we use the variational method to determine the existence of the ground state solutions of equation (1.1). And it is proved that if λâ†'∞, the corresponding convergent point is ground state solutions of (1.2).(1.2) is the following form...