Directory UMM :Journals:Journal_of_mathematics:EJQTDE:

Electronic Journal of Qualitative Theory of Differential Equations
2011, No. 32, 1-11; http://www.math.u-szeged.hu/ejqtde/

Boundary layer analysis for nonlinear
singularly perturbed differential
equations
Robert Vrabel1, ∗, Vladimir Liska1 and Ingrid Mankova1
1 Institute of Applied Informatics, Automation
and Mathematics
Faculty of Materials Science and Technology
Hajdoczyho 1, 917 01 Trnava, Slovakia

Abstract
This paper focuses on the boundary layer phenomenon arising in
the study of singularly perturbed differential equations. Our tools include the method of lower and upper solutions combined with analysis
of the integral equation associated with the class of nonlinear equations under consideration.
Key words and phrases: singularly perturbed systems, three–point
boundary value problem, method of lower and upper solutions.
AMS Subject Classifications: 34E15, 34A34, 34A40, 34B10

1

Introduction

This paper is devoted to study the second-order semilinear singularly
perturbed differential equation
ǫy ′′ + ky = f (t, y),

t ∈ [a, b],

k