The Existence Of Standing Wave Of Chern-Simons-Schr(?)dinger Equations With Non-radial Symmetry Potential

In this paper,we consider the following Chern-Simons-Schrodinger equations:(?)where N:R1,2→R is a neutral scalar field,the parameters κ,q>0 in the equations(0.0.2)represent the Chern-Simons coupling constant and the Maxwell coupling constant respectively.Moreover,the potential V(x)is a function from R2 to R.Suppose V(x)satisfies the following conditions:(V1)lim|x|→+∞ V(x)=1,(V2)0<V0≤V(x)≤1,mes{x,V(x)≠1}>0.We show the existence of a standing wave solution for the equations(0.0.2).This thesis is divided into three chapters.In chapter 1,we introduce the background of the problem and main results of the thesis.In chapter 2,we give some preliminaries and the related lemmas with their proofs.In chapter 3,under the assumption(V1)and(V2),we show the existence of a standing wave solution for the equations(0.0.2)by using the variational method.