A class of boundary value problems for four-order nonlinear singular perturbation equation

Using the matching asymptotic expansion method,a class of singularly perturbed boundary value problems with two boundary layers for forth-order nonlinear equation is studied.Introducing the stretched variables,according to the boundary conditions and the matching principle,under the definite solvability conditions,the outer solution and the interior solution near the left and right boundary layers are given.The asymptotic solution with second-order for the problem is obtained.The existence of the solution for this class of nonlinear problems is illustrated by an example.