THE DIRICHLET-PROBLEM FOR A SINGULAR SINGULARLY PERTURBED QUASI-LINEAR 2ND-ORDER DIFFERENTIAL SYSTEM

In this paper, we study the ''multi-layer'' phenomenon of the Dirichle t problem for a singular singularly perturbed second order vector syst em epsilon dz(2)/dt(2) = F(z, t) dz/dt + g(z, t) under the key assumpt ion 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 exam ple. (C) 1997 Academic Press.