Oscillation of equations with an infinite distributed delay

Leonid Berezansky; Elena Braverman

doi:10.1016/j.camwa.2010.08.071

Oscillation of equations with an infinite distributed delay

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

11 Scopus citations

Abstract

For the equation with a finite or infinite distributed delay x(t)+∫-∞tx(s)dsR(t,s)=0 the existence of nonoscillatory solutions is studied. A general comparison theorem is obtained which allows to compare oscillation properties of equations with concentrated delays to integrodifferential equations. Sharp nonoscillation conditions are deduced for some autonomous integrodifferential equations. Using comparison theorems, an example is constructed where oscillation properties of an integrodifferential equation are compared to equations with several concentrated delay which can be treated as its finite difference approximations.

Original language	English
Pages (from-to)	2583-2593
Number of pages	11
Journal	Computers and Mathematics with Applications
Volume	60
Issue number	9
DOIs	https://doi.org/10.1016/j.camwa.2010.08.071
State	Published - 1 Nov 2010

Keywords

Comparison theorems
Distributed delay
Infinite delay
Integrodifferential equations
Oscillation

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2010.08.071

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AB - For the equation with a finite or infinite distributed delay x(t)+∫-∞tx(s)dsR(t,s)=0 the existence of nonoscillatory solutions is studied. A general comparison theorem is obtained which allows to compare oscillation properties of equations with concentrated delays to integrodifferential equations. Sharp nonoscillation conditions are deduced for some autonomous integrodifferential equations. Using comparison theorems, an example is constructed where oscillation properties of an integrodifferential equation are compared to equations with several concentrated delay which can be treated as its finite difference approximations.

KW - Comparison theorems

KW - Distributed delay

KW - Infinite delay

KW - Integrodifferential equations

KW - Oscillation

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Oscillation of equations with an infinite distributed delay

Abstract

Keywords

ASJC Scopus subject areas

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