The Overlaping Layer Solution to Nonlinear Singularly Perturbed Boundary Value Problem

A singularly perturbed problem of the nonlinear equation is considered. Under suitable conditions, using the stretched variables the formal asymptotic expansion with the overlapping layer, a solution to is provided. And using the theory of differential inequalities, the uniformly valid behavior of its expansion is proved. The method and the result is meaningful for the study of nonlinear singularly perturbed boundary value problems.