The Dirichlet Problem for a Singular Singularly Perturbed Quasilinear Second Order Differential System*

In this paper, we study the ‘‘multi-layer’’ phenomenon of the Dirichlet problem for a singular singularly perturbed second order vector system « dz2rdt 2s F z, t. dzrdtqg z, t. under the key assumption that the corresponding reduced system is a differential algebraic system of index 1. The formal asymptotic solutions exhibiting multiple boundary layers at one endpoint were constructed and proved uniformly valid. The constructive methods were illustrated by a nontrivial example