Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation
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 e...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2000-07-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/56/abstr.html |
| Summary: | 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. |
|---|---|
| ISSN: | 1072-6691 |