## Oscillation of first order delay differential equations.(English)Zbl 0865.34057

Summary: We introduce a new technique to analyze generalized characteristic equations to obtain some infinite integral conditions for oscillations of nonautonomous delay differential equations.

### MSC:

 34K11 Oscillation theory of functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

### Keywords:

oscillation; nonoscillation; delay differential equations
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### References:

 [1] M. I. Tramov, Conditions for the oscillation of the solutions of first order differential equations with retarded argument, Izv. Vysš. Učebn. Zaved. Matematika 3(154) (1975), 92 – 96 (Russian). · Zbl 0319.34070 [2] Gerasimos Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), no. 2, 93 – 98. · Zbl 0407.34055 [3] R. G. Koplatadze and T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial$$^{\prime}$$nye Uravneniya 18 (1982), no. 8, 1463 – 1465, 1472 (Russian). · Zbl 0496.34044 [4] G. Ladas and I. P. Stavroulakis, Oscillations caused by several retarded and advanced arguments, J. Differential Equations 44 (1982), no. 1, 134 – 152. · Zbl 0452.34058 [5] O. Arino, I. Győri, and A. Jawhari, Oscillation criteria in delay equations, J. Differential Equations 53 (1984), no. 1, 115 – 123. · Zbl 0547.34060 [6] Brian R. Hunt and James A. Yorke, When all solutions of \?$$^{\prime}$$=-\sum \?\?(\?)\?(\?-\?\?(\?)) oscillate, J. Differential Equations 53 (1984), no. 2, 139 – 145. · Zbl 0571.34057 [7] M. K. Grammatikopoulos, E. A. Grove, and G. Ladas, Oscillations of first-order neutral delay differential equations, J. Math. Anal. Appl. 120 (1986), no. 2, 510 – 520. · Zbl 0566.34056 [8] István Győri, Oscillation conditions in scalar linear delay differential equations, Bull. Austral. Math. Soc. 34 (1986), no. 1, 1 – 9. · Zbl 0585.34044 [9] G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation theory of differential equations with deviating arguments, Monographs and Textbooks in Pure and Applied Mathematics, vol. 110, Marcel Dekker, Inc., New York, 1987. · Zbl 0832.34071 [10] B. G. Zhang and K. Gopalsamy, Oscillation and nonoscillation in a nonautonomous delay-logistic equation, Quart. Appl. Math. 46 (1988), no. 2, 267 – 273. · Zbl 0648.34078 [11] G. Ladas and C. Qian, Oscillation in differential equations with positive and negative coefficients, Canad. Math. Bull. 33 (1990), no. 4, 442 – 451. · Zbl 0723.34068 [12] Yuan Ji Cheng, Oscillation in nonautonomous scalar differential equations with deviating arguments, Proc. Amer. Math. Soc. 110 (1990), no. 3, 711 – 719. · Zbl 0736.34060 [13] I. Győri and G. Ladas, Oscillation theory of delay differential equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. With applications; Oxford Science Publications. · Zbl 0780.34048 [14] Man Kam Kwong, Oscillation of first-order delay equations, J. Math. Anal. Appl. 156 (1991), no. 1, 274 – 286. · Zbl 0727.34064 [15] G. Ladas, C. Qian, and J. Yan, A comparison result for the oscillation of delay differential equations, Proc. Amer. Math. Soc. 114 (1992), no. 4, 939 – 947. · Zbl 0748.34044 [16] B. Li, Oscillations of delay differential equations with variable coefficients, J. Math. Anal. Appl. 192 (1995), 312-321. CMP 95:12 [17] L. H. Erbe, Qingkai Kong and B. G. Zhang, Oscillation theory for functional differential equations, Marcel Dekker, New York, 1995. CMP 95:6 · Zbl 0821.34067
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