For the scalar delay differential equation with a distributed delay
a connection between the properties
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.
Cite this article
Leonid Berezansky, Elena Braverman, On Oscillation of Equations with Distributed Delay. Z. Anal. Anwend. 20 (2001), no. 2, pp. 489–504DOI 10.4171/ZAA/1026