Asymptotic Solutions for a Class of Nonlinear Singularly Perturbed Boundary Value Problems

A class of nonlinear singularly perturbed problems with parameter is discussed using the matching asymptotic expanding method.Firstly,the outer solutions to satisfy the degenerate equation are found.The inner solutions expressed with special function are gotten as the five different cases of parameter,then the conclusion that the problem must have one of the boundary layers at left,right and interior(where the left boundary layer has two different cases and also the right) is obtained.Finally,zero-order uniformly valid asymptotic expansions of the problem are given by matching the outer and inner solutions according to the matching principle.