On Solutions Of A Class Of Semilinear Schr(?)dinger Equation

With the rapid development of science and technology,the differential equation has attracted more and more attention.It has a wide range of applications in physics,geom-etry,optics,quantum mechanics and other fields.In this paper,we consider the existence of high energy solutions and small energy solutions of a class of nonlinear Schr(?)dinger equation,the main content is arranged as followsIn the first chapter,we first briefly introduce variational method and critical point theory,then we introduce the development of the research of solutions for Schr(?)dinger equation in the whole space,then a brief account of the main work to this article is given,finally we give some preliminary knowledge and notationsIn the second chapter,we discuss the existence of high energy solutions for a class of Schr(?)dinger equation with sign-changing potentials,and the nonlinearity satisfies su-perquadratic growth conditions.We use Fountain Theorem to establish the existence of high energy solutions for such equation,the results of this chapter generalize conclusions of existent literatureIn the third chapter,we consider a class of semilinear Schr(?)dinger equation with pos-itive and continuous potential.By using Dual Fountain Theorem,we prove the existence of small energy solutions under proper conditions for the problemIn the last chapter,we summary the full text,and give some prospects and thoughts on related issues.