Existence Of Solutions For A Class Of Ginzburg-Landau Vortex Equations

In this thesis,we study the existence of solutions for a class of Ginzburg-Landau vortex equations.For Ginzburg-Landau equations,there are important applications in superconductivity and other fields.There have been abundant results of Ginzburg-Landau equations for single component.However,there are few results for two components.We mainly study the existence of solutions for a class of two components Ginzburg-Landau model and establish the existence theory of radial symmetric solutions.The equations are derived from the Lagrangian density of the model,then the problem is transformed into solving the partial differential equations.For radial symmetric solutions of the model,the partial differential equations are transformed into ordinary differential equations and the boundary value problem is transformed into the initial value problem.According to the shooting method and the schauder fixed point theorem,we prove the existence of the radial symmetric solutions of the model.Moreover,we establish the asymptotic estimate of the solution and the quantized integral.