Existence Of Monopoles In AdS Spacetime

In this paper, we study the existence of monopoles in anti-de Sitter (AdS) spacetime.The whole paper consists of two chapters. The mathematical structure and the main results of the problem are introduced in chapter 1. The main results are proved in chapter 2. For the given special potential function, we prove the existence of the solution of the problem by shooting method and give the asymptotic estimate of the solution at infinity.For the potential function of the general form, two cases are considered. A situation is the potential function has only one zero point, we prove the existence of the solution by the shooting method. The other is the potential function has only two zero points, we prove the existence of the solution by the variational method and get the relevant properties of the solution.