A Robin Problem For The Semilinear Perturbed ODE System

In this paper, using the method of boundary functions, the Robin prpblem of a class of semi linear perturbed equations was studied as followsWhere y, A and B are all n-dimensional vectors, h is n-dimensionalvector function in the R~n×[0,1] and P,Q are both n×n matrix.In chapter 1, we simply introduced the development in singular perturbation, and introduce the work that has been done. In chapter 2, first we list the prepare knowledge,then we discuss the above problem, the method of boundary function was used to construst the uniformly valid asymptotic solutions of the problem we discussed. At the same time the existence and uniqueness of solution and the estimation of remainder for the problem are given. Also an example is raised to support our results. In chapter 3, by showing some similar problems for the readers to think about and work it out.