Study On The Existence Of Solutions For Two Types Of Nonlinear Ordinary Differential Equations Arising In Field Theory

In this paper,we mainly study the existence of solutions for two types of models in classical field theory.In the first part,the Sakurai model appearing in the Skyrme theory is transformed into a two-point boundary value problem of nonlinear ordinary differential equation by an appropriate Ansatz.And then we establish the existence of solutions for this problem by using variational method and shooting method,in addition,the asymptotic estimates of the solutions at the endpoints are given.In the second part,we concentrate on studying the Goldstone model which appears in the gauge field theory.The problem can also be transformed into a two-point boundary value problem of nonlinear ordinary differential equation by an appropriate Ansatz.Then we prove the existence and uniqueness of the vortex solution by variational method,analytical method and shooting method respectively,and also present the asymptotic estimates at the endpoints and related properties.