On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays. (30th August 2010)

• Record Type: Journal Article
• Authors: Baštinec, Jaromír; Berezansky, Leonid; Diblík, Josef; Šmarda, Zdeněk
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2010(2010)
• Publication Date: 2010-08-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2010/417869
• Languages: English
• ISSNs: 1085-3375

Abstract

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