JournalszaaVol. 20, No. 2pp. 489–504

On Oscillation of Equations with Distributed Delay

  • Leonid Berezansky

    Ben Gurion University of the Negev, Beer-Sheba, Israel
  • Elena Braverman

    Technion - Israel Institute of Technology, Haifa, Israel
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Abstract

For the scalar delay differential equation with a distributed delay

x˙(t)+tx(s)dsR(t,s)=f(t)(t>to)\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.

Cite this article

Leonid Berezansky, Elena Braverman, On Oscillation of Equations with Distributed Delay. Z. Anal. Anwend. 20 (2001), no. 2, pp. 489–504

DOI 10.4171/ZAA/1026