Abstract and Applied Analysis

On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays

Jaromír Baštinec, Leonid Berezansky, Josef Diblík, and Zdeněk Šmarda

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 417869, 20 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620771

Digital Object Identifier
doi:10.1155/2010/417869

Mathematical Reviews number (MathSciNet)
MR2720031

Zentralblatt MATH identifier
1209.34080

Citation

Baštinec, Jaromír; Berezansky, Leonid; Diblík, Josef; Šmarda, Zdeněk. On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays. Abstr. Appl. Anal. 2010 (2010), Article ID 417869, 20 pages. doi:10.1155/2010/417869. https://projecteuclid.org/euclid.aaa/1288620771


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