On The Existence Of Solutions For Schrodinger Equations

Nonlinear problems in mathematics originated from physics, chemistry, biology, celestial mechanics, economic and social science. It is manifested in the form of a variety of nonlinear equations. So, the mathematical word and the science world attach importance to the nonlinear functional analysis. With the development of science and technology, some new results for the nonlinear functional analysis and its applications have been obtained. The existence of solutions for a class of Schrodinger equations is one of the hot spots which has been discussed in recent years. In this paper, under the Cerami condition, we use the mountain pass theory to study the existence of solutions for several kinds of Schrodinger equations.The thesis is divided into there sections according to contents.Chapter1Preference, we introduce the main contents of this paper.Chapter2In this chapter we mainly study the nonhomogeneous Schrodinger equation where f∈C(R) and By using Mountain-Pass Theorem, we prove the existence of a nontrivial solution.Chapter3The purpose of this work is to deal with the existence of solution for the following quadratic Schrodinger equations where V∈C(RN, R), H1(RN) is the usual Sobolev space, and f∈C(RN x R, R) where F(x, u)=∫0uf(x, t)dt. Moreover, F is superquadratic at the origin and asymptotically at infinity.