Ordinary Differential Equations
Many of the problems in two dimensions involve the Dirac function type singular source terms. The purpose of this chapter is to present a systematic study of one of the simplest such problems, namely, the radially symmetric solutions of a general scalar equation. In §9.1, we state our existence results. In §9.2, we present a dynamical analysis of all possible solutions. In §9.3, we show how to apply our results to obtain a complete understanding of symmetric Chern—Simons vortices. We shall later show that the results may be used to achieve a deep understanding of cosmic string solutions in terms of the string number and the universal gravitational constant.
KeywordsOrdinary Differential Equation Cosmic String String Solution Vortex Solution String Number
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