Oscillation of equations with an infinite distributed delay

Authors:
Leonid Berezansky;Elena Braverman
Affiliations:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 1
Cited 1

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On the existence of positive solutions for systems of differential equations with a distributed delay

Computers & Mathematics with Applications

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Abstract

For the equation with a finite or infinite distributed delay x@?(t)+@!"-"~^tx(s)d"sR(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.