Advanced Search

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]