Periodic Solutions of Periodic Retarded Functional Differential Equations
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 353-363
MSC: Primary 34K13.
DOI: 10.4064/ba52-4-2
Abstract
The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x'(t) = f(t, x_{t})$, where $f$ is $T$-periodic in $t$. We construct a pair of subsets of ${\mathbb R} \times {\mathbb R}^{n}$ called a $T$-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a $T$-periodic solution.
