## Abstract and Applied Analysis

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

#### Abstract

New nonoscillation and oscillation criteria are derived for scalar delay differential equations $\dot{x}(t)+a(t)x(h(t))=0,a(t)\geq 0,h(t)\leq t,t\geq {t}_{0},$ and $\dot{x}(t)+\sum_{k=1}^{m}{a}_{k}(t)x({h}_{k}(t))=0,{a}_{k}(t)\geq 0,{h}_{k}(t)\leq t,$ and $t\geq {t}_{0},$ 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