Existence Of Sign-changing Solutions For The Gauged Nonlinear Chern-Simons-Schr(?)dinger Systems

In this thesis,we investigate the existence of sign-changing solutions to several types of gauged nonlinear Schr(?)dinger systems including Chern-Simons term,by using variational methods,the existence and multiple solutions of these systems are obtained.It is organized as follows:We give a brief introduction to the background and research status of our problems.Meanwhile,some related lemmas are given,the main results obtained in this thesis are also presented.Firstly,we investigate the existence and multiplicity of sign-changing solutions to the class of nonlinear Schr(?)dinger systems with ChernSimons term by the method of invariant sets of descending flow and a general critical point theory.And then we study the existence and multiplicity of sign-changing solutions to the class of nonlinear Schr(?)dinger systems with Chern-Simons term via a novel perturbation approach and the method of invariant sets of descending flow.Moreover,we consider the existence and multiplicity of sign-changing solutions to the nonlinear Schr(?)dinger systems of kequations with Chern-Simons term by the method of invariant sets of descending flow.In the end,we summarize the results of this thesis and make some discussions.