×

zbMATH — the first resource for mathematics

Oscillation of first-order delay equations. (English) Zbl 0727.34064
The author studies the oscillation of first order delay differential equations using a method that parallels the use of Riccati equations in the study of the oscillation of second order ordinary differential equations without delay. The author gives an alternative proof of a comparison theorem first established by Kwong and Patula, obtains some results on the asymptotic behavior of nonoscillatory solutions, proves a new criterion that falls within a gap left open by established results, and confirms a conjecture raised by B. R. Hunt and J. A. Yorke [J. Differ. Equations 53, 139-145 (1984; Zbl 0571.34057)].

MSC:
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
PDF BibTeX Cite
Full Text: DOI
References:
[1] Hunt, B.R; Yorke, J.A, When all solutions of x′ = − ∑qi(t)x(t − ti(t)) oscillate, J. differential equations, 53, 139-145, (1984) · Zbl 0571.34057
[2] Kwong, M.K; Patula, T, Comparison theorem for first order linear delay equations, J. differential equations, 70, 275-292, (1987) · Zbl 0653.34048
[3] Ladde, G.S; Lakshmikantham, V; Zhang, B.G, Oscillation theory of differential equations with deviating arguments, (1987), Dekker New York · Zbl 0832.34071
[4] Ladas, G; Stavroulakis, I.P, Oscillations caused by several retarded and advanced arguments, J. differential equations, 44, 134-152, (1982) · Zbl 0452.34058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.