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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 {\it B. R. Hunt} and {\it J. A. Yorke} [J. Differ. Equations 53, 139-145 (1984; Zbl 0571.34057)].

##### MSC:
 34K99 Functional-differential equations 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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##### References:
 [1] Hunt, B. R.; Yorke, J. A.: When all solutions of x’ = - $sumqi(t)$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) · 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