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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)].

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
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[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
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