Existence Of Infinitely Many Small Energy Solutions For The Chern-Simons-Schr(?)dinger Equations

In the early 1990s of the last century,Chern-Simons-Schr(?)dinger system was proposed by Jackiw and Pi.It describes a planer charged particle confined by a harmonic oscillator potential in the background of a perpendicular magnetic field.This feature of the model is important for the study of the high-temperature su-perconductor,Aharovnov-Bohm scattering,and quantum Hall effect.In this paper,we study the Chern-Simons-Schr(?)dinger system by using the variational methods in R2.We consider the following nonlinear Chern-Simons-Schr(?)dinger equation with the lower perturbation term-?u+?u+(h2(|x|)/|x|2+?|x|?h(s)/sds)u=??(|x|)|u|q-2u+g(|x|,u),x?R2,where ??0,q?(1,2),?:R2?(0,+?)???L2/2-q(R2)?C(R2),g(|x|,u)is supcrlincar in u at infinity.By applying the variant fountain theorem,the infinitely many small energy solutions for the equations are obtained.This thesis consists of two chapters.The first chapter is devoted to discuss the introduction including research background and prerequisite knowledge.The second chapter deals with the multiplicity of the solutions for the nonlinear Chern-Simons-Schr(?)dinger equation with the lower perturbation term,the main conclusion is theorem 2.1.