## Differential and Integral Equations

### Periodic solutions of delay equations with several fixed delays

Benjamin Kennedy

#### Abstract

We present an existence result for periodic solutions of autonomous differential delay equations with several fixed delays \begin{eqnarray*} x'(t) = \sum_{i=1}^D f_i (x(t - d_i)), \end{eqnarray*} where the functions $f_i$ are close to two-valued step functions $h_i$. We give conditions under which existence of periodic solutions of the more tractable problem $$y'(t) = \sum_{i=1}^D h_i (y(t - d_i))$$ implies the existence of similar periodic solutions of the original problem. Our approach is to show that an analog of a Poincaré map has non-trivial fixed-point index.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 7/8 (2009), 679-724.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019544

Mathematical Reviews number (MathSciNet)
MR2532117

Zentralblatt MATH identifier
1240.34317

Subjects
Primary: 34K13: Periodic solutions

#### Citation

Kennedy, Benjamin. Periodic solutions of delay equations with several fixed delays. Differential Integral Equations 22 (2009), no. 7/8, 679--724. https://projecteuclid.org/euclid.die/1356019544