The Asymptotic Solution For A Kind Of Quadradic Nonlinear Singular Perturbation Robin Problems

In this paper, the asymptotic solution for a kind of quadradic nonlinear singular perturbation robin problemsis given by the method of boundary functions, and its uniform validity is discussed under some conditions, more over, The n_th-order asymptotic estimate is obtained.In section 1, we simply introduced the development in singular perturbation, and introduce the work that has been done. In section 2, the problems to be solved are presented at first, the method of boundary function was used to construst the uniformly valid asymptotic solutionsof the problems we discussed. At the same time the existence and uniquenessof solution and the estimation of remainder for the problems aregiven. And, some interrelated problems are shown for the readers to think about and work out.In section 3, an example is raised to support our results.