The Existence Of Multivortex Solutions In The Self-Dual Maxwell-Higgs Model

In this thesis,we study the existence of self-dual vortex solutions for a class of generalized Maxwell-Higgs model.We have proved the existence of non-topological solutions and radial symmetric solutions for the corresponding BPS vortex equations.The existence of general non-topological solutions is proved by using the implicit function theorem.And we give the asymptotic estimates of the solution at infinity.According to the shooting method,we prove the existence of radial symmetric solutions.And we give the uniqueness of radial symmetric topological solutions and the asymptotic behavior of radial symmetric non-topological solutions at infinity.