On oscillation of a differential equation with infinite number of delays

L. Berezansky; E. Braverman

doi:10.4171/ZAA/1109

On oscillation of a differential equation with infinite number of delays

L. Berezansky
, E. Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For a scalar delay differential equation ẋ(t) + ∑_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.

Original language	English
Pages (from-to)	803-816
Number of pages	14
Journal	Zeitschrift für Analysis und ihre Anwendungen
Volume	21
Issue number	3
DOIs	https://doi.org/10.4171/ZAA/1109
State	Published - 1 Jan 2002

Keywords

Delay differential equations
Infinite number of delays
Non-oscillation
Oscillation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.4171/ZAA/1109

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AB - For a scalar delay differential equation ẋ(t) + ∑k=1∞ak(t)x(hk(t)) = 0 (hk(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.

KW - Delay differential equations

KW - Infinite number of delays

KW - Non-oscillation

KW - Oscillation

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On oscillation of a differential equation with infinite number of delays

Abstract

Keywords

ASJC Scopus subject areas

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