천 사이먼스 슈뢰딩거 방정식의 정상파에 관하여

Abstract

In this dissertation, we study standing waves for the Chern-Simons-Schr oedinger equations. Some existence results of standing waves are established by applyingvariational methods to the functional which is obtained by representing the gauge field in terms of the complex scalar field. We also show that there exist no standing waves for certain range or parameters by establishing a newinequality of Sobolev type.