Existence Of Solutions For A Class Of Self-Dual Chern-Simons Vortex Equations

In this thesis,we study the existence of solutions for a class of generalized Chern-Simons model.We establish the existential theory of radial symmetric solutions and non-topological solutions.The BPS equations are derived from the Lagrangian density of the model,then the problem is transformed into solving the partial differential equation.For radial symmetric solutions,the boundary value problem is transformed into the initial value problem.We construct five sets of parameters.According to the shooting method,we prove the existence of the radial symmetric solutions.For general non-topological solutions,the approximate solution of the equation is constructed by using the explicit solution of the Liouville equation.The equation which the error term satisfies is transformed into the corresponding functional equation,so we define the mapping.The existence of general non-topological solutions is proved by using the implicit function theorem.And we give the asymptotic estimate of the solution at infinity.