Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 56, pp. 1-18.
Title: Uniqueness of rapidly oscillating periodic solutions to a
singularly perturbed differential-delay equation
Author: Hari P. Krishnan (Chicago, IL, USA)
Abstract:
In this paper, we prove a uniqueness theorem for rapidly oscillating
periodic solutions of the singularly perturbed differential-delay
equation
$\varepsilon \dot{x}(t)=-x(t)+f(x(t-1))$.
In particular, we show that, for a given oscillation rate,
there exists exactly one periodic solution to the above equation.
Our proof relies upon a generalization of Lin's method, and is valid
under generic conditions.
Submitted December 1, 1999. Published July 24, 2000.
Math Subject Classifications: 34K26, 37G10.
Key Words: delay equation; rapidly oscillating; singularly perturbed.