The Infinite Initial Value Problem And Boundary Value Problem For A Kind Of Second-order Quasi-linear System In The Critical Case

In this paper,we mainly discuss a class of second-order quasi-linear system :which is in the critical case, with infinite initial value or boundary value. In chapter 1, we simply introduce some developments in singular perturbation of ODE in the critical case, list the preparing knowledge and introduce the work has been down. In chapter 2, for a class of special square matrixwe discuss the above second-order quasi-linear system with infinite initial valuesWe not only give algorithm for the formal asymptotic solution, but also prove the existence and uniqueness of the solution of the system and estimate the remainder term. Also an example is raised to support our point. In chapter 3,we discuss the case in which the above system should satisfy the Dirichlet boundary values. In chapter 4, we extend the foregoing problems forward for the readers to think about and work it out.