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.