The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (207 KB) | Metadata | Table of Contents | ZAA summary
Volume 21, Issue 3, 2002, pp. 803–816
DOI: 10.4171/ZAA/1109

Published online: 2002-09-30

On Oscillation of a Differential Equation with Infinite Number of Delays

Leonid Berezansky[1] and Elena Braverman[2]

(1) Ben Gurion University of the Negev, Beer-Sheba, Israel
(2) Technion - Israel Institute of Technology, Haifa, Israel

For a scalar delay differential equation $$\dot{x}(t) + \sum^\infty_{k=1} a_k(t)x(h_k(t)) = 0 \; \; \; (H_k(t) ≤ t)$$ a connection between the following four properties is established:
- non-oscillation of this equation
- non-oscillation of the corresponding differential inequality
- positiveness of the fundamental function - existence of a non-negative solution for a certain explicitly constructed nonlinear integral inequality.
Explicit non-oscillation and oscillation conditions, comparison theorems and a criterion of the existence of a positive solution are presented for this equation.

Keywords: Delay differential equations, infinite number of delays, oscillation, non-oscillation

Berezansky Leonid, Braverman Elena: On Oscillation of a Differential Equation with Infinite Number of Delays. Z. Anal. Anwend. 21 (2002), 803-816. doi: 10.4171/ZAA/1109