Introduction

Abstract

We are mainly interested in quasilinear and nonlinear boundary value problems, to which some well-known methods, such as the methods of matched asymptotic expansions and two-variable expansions are not immediately applicable. For example, let us consider the following boundary value problem(cf. O’Malley [75], Chapter 5)

$$ \varepsilon y'' = y'^2 , 0 < t < 1, $$

(A)

$$ y(0,\varepsilon ) = 1, y(1,\varepsilon ) = 0. $$

(B)