# Semilinear Singular Perturbation Problems

• K. W. Chang
• F. A. Howes
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 56)

## Abstract

We consider first the semilinear Dirichlet problem

$$\begin{gathered} \varepsilon y'' = h(t,y), a < t < b, \hfill \\ y(a,\varepsilon ) = A, y(b,\varepsilon ) = B, \hfill \\ \end{gathered}$$
(DP1)

where e is a small positive parameter and prime denotes differentiation with respect to t. Some natural questions to ask regarding this problem are: Does the problem have a solution for all small values of ε? Once the existence of a solution has been established, how does the solution behave as ε + 0+?

## Keywords

Positive Constant Dirichlet Problem Stable Solution Shock Layer Fixed Constant
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