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2010 On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays
Jaromír Baštinec, Leonid Berezansky, Josef Diblík, Zdeněk Šmarda
Abstr. Appl. Anal. 2010: 1-20 (2010). DOI: 10.1155/2010/417869

Abstract

New nonoscillation and oscillation criteria are derived for scalar delay differential equations x ˙ ( t ) + a ( t ) x ( h ( t ) ) = 0 , a ( t ) 0 , h ( t ) t , t t 0 , and x ˙ ( t ) + k = 1 m a k ( t ) x ( h k ( t ) ) = 0 , a k ( t ) 0 , h k ( t ) t , and t t 0 , in the critical case including equations with several unbounded delays, without the usual assumption that the parameters a , h , a k , and h k of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.

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Jaromír Baštinec. Leonid Berezansky. Josef Diblík. Zdeněk Šmarda. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays." Abstr. Appl. Anal. 2010 1 - 20, 2010. https://doi.org/10.1155/2010/417869

Information

Published: 2010
First available in Project Euclid: 1 November 2010

zbMATH: 1209.34080
MathSciNet: MR2720031
Digital Object Identifier: 10.1155/2010/417869

Rights: Copyright © 2010 Hindawi

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