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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 2, 2001, pp. 489–504
DOI: 10.4171/ZAA/1026

Published online: 2001-06-30

On Oscillation of Equations with Distributed Delay

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 the scalar delay differential equation with a distributed delay $$\dot{x} (t) + \int ^t_{– \infty} x(s)d_sR(t,s) = f(t) (t > t_o)$$ a connection between the properties
non-oscillation
positiveness of the fundamental function
existence of a non-negative solution for a certain nonlinear integral inequality
is established. This enables to obtain comparison theorems and explicit non-oscillation and oscillation conditions being generalizations of some known results for delay equations and integro-differential equations and leads to oscillation results for equations with infinite number of delays.

Keywords: Oscillation, non-oscillation, distributed delay, comparison theorems

Berezansky Leonid, Braverman Elena: On Oscillation of Equations with Distributed Delay. Z. Anal. Anwend. 20 (2001), 489-504. doi: 10.4171/ZAA/1026