Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0918.34066
Li, Jibin; He, Xue-Zhong
Multiple periodic solutions to differential delay equations created by asymptotically linear Hamiltonian systems.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 31, No.1-2, 45-54 (1998). ISSN 0362-546X

The author considers the following differential delay equation\par $$x'(t)=\sum_{i=1}^n(-1)^{[il/n]}f(x(t-r_i)), \quad 1\le l\le n-1,$$ where $l$ and $n$ are relatively prime, $r_i$ are positive constants and $[]$ denotes the integer part. Assuming that $f\in C^1$ is an odd function with positive derivative and $f(x)/x$ converges as $x$ tends to $+\infty ,$ some existence and multiplicity results for periodic solutions are proved. As a corollary these results yield to a proof of a conjecture due to {\it J. L. Kaplan} and {\it J. A. Yorke} [J. Math. Anal. Appl. 48, 317-324 (1974; Zbl 0293.34102)].
[Marcos Lizana (Tempe)]
MSC 2000:
*34K13 Periodic solutions of functional differential equations
34C25 Periodic solutions of ODE
34K05 General theory of functional-differential equations

Keywords: periodic solutions; delay equations; Hamiltonian systems

Citations: Zbl 0293.34102

Highlights
Master Server