JournalszaaVol. 21, No. 3pp. 803–816

On Oscillation of a Differential Equation with Infinite Number of Delays

  • Leonid Berezansky

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

    Technion - Israel Institute of Technology, Haifa, Israel
On Oscillation of a Differential Equation with Infinite Number of Delays cover
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Abstract

For a scalar delay differential equation

x˙(t)+k=1ak(t)x(hk(t))=0      (Hk(t)t)\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.

Cite this article

Leonid Berezansky, Elena Braverman, On Oscillation of a Differential Equation with Infinite Number of Delays. Z. Anal. Anwend. 21 (2002), no. 3, pp. 803–816

DOI 10.4171/ZAA/1109