zbMATH — the first resource for mathematics

New oscillation criterion for delay differential equations with non-monotone arguments. (English) Zbl 1331.34132
Summary: We investigate the oscillation of a first order delay differential equation with non-negative coefficient and non-monotone arguments. New oscillation criterion of lim sup type is obtained. An example is given to show the applicability and strength of the obtained condition over known ones.

MSC:
 34K11 Oscillation theory of functional-differential equations
Full Text:
References:
 [1] Myshkis, A. D., Linear homogeneous differential equations of first order with deviating arguments, Uspekhi Mat. Nauk, 5, 160-162, (1950), (in Russian) · Zbl 0041.42108 [2] Braverman, E.; Karpuz, B., On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput., 218, 3880-3887, (2011) · Zbl 1256.39013 [3] El-Morshedy, H. A., On the distribution of zeros of solutions of first order delay differential equations, Nonlinear Anal., 74, 3353-3362, (2011) · Zbl 1218.34078 [4] Erbe, L. H.; Zhang, B. G., Oscillation for first order linear differential equations with deviating arguments, Differential Integral Equations, 1, 305-314, (1988) · Zbl 0723.34055 [5] Elbert, Á.; Stavroulakis, I. P., Oscillations of first order differential equations with deviating arguments, (Recent Trends in Differential Equations, (1992), World Scientific Publishing Co) · Zbl 0832.34064 [6] Jaros, J.; Stavroulakis, I. P., Oscillation tests for delay equations, Rocky Mountain J. Math., 29, 197-207, (1999) · Zbl 0938.34062 [7] Karpuz, B., Oscillation of first-order differential equations with retarded arguments, Math. Slovaca, 62, 247-256, (2012) · Zbl 1274.34194 [8] Koplatadze, R. G.; Chanturija, T. A., On oscillatory and monotonic solutions of first order differential equations with deviating arguments, Differ. Uravn., 18, 1463-1465, (1982), (in Russian) · Zbl 0496.34044 [9] Koplatadze, R. G.; Kvinikadze, G., On the oscillation of solutions of first order delay differential inequalities and equations, Georgian Math. J., 1, 675-685, (1994) · Zbl 0810.34068 [10] Kon, M.; Sficas, Y. G.; Stavroulakis, I. P., Oscillation criteria for delay equations, Proc. Amer. Math. Soc., 128, 2989-2997, (2000) · Zbl 0951.34045 [11] Kwong, M. K., Oscillation of first order delay equations, J. Math. Anal. Appl., 156, 274-286, (1991) · Zbl 0727.34064 [12] Ladas, G.; Lakshmikantham, V.; Papadakis, J. S., Oscillations of higher-order retarded differential equations generated by the retarded argument, (Delay and Functional Differential Equations and Their Applications (Proc. Conf., Park City, Utah, 1972), (1972), Academic Press New York) · Zbl 0273.34052 [13] Philos, Ch. G., On the existence of nonoscillatory solutions tending to zero at $$\infty$$ for differential equations with positive delays, Arch. Math. (Basel), 36, 168-178, (1981) · Zbl 0463.34050 [14] Philos, Ch. G.; Sficas, Y. G., An oscillation criterion for first-order linear delay differential equations, Canad. Math. Bull., 41, 207-213, (1998) · Zbl 0922.34060 [15] Sficas, Y. G.; Stavroulakis, I. P., Oscillation criteria for first-order delay equations, Bull. Lond. Math. Soc., 35, 239-246, (2003) · Zbl 1035.34075 [16] Stavroulakis, I. P., Oscillation criteria for delay and difference equations with non-monotone arguments, Appl. Math. Comput., 226, 661-672, (2014) · Zbl 1354.34120 [17] Stavroulakis, I. P., A survey on the oscillation of differential equations with several deviating arguments, J. Inequal. Appl., 2014, 399, (2014) · Zbl 1372.34105 [18] Zhao, A.; Tang, X. H; Yan, J., Oscillation of first-order delay differential equations, ANZIAM J., 45, 593-599, (2004) · Zbl 1056.34064 [19] Zhou, Y.; Yuanhong, Y., On the oscillation of solutions of first order differential equations with deviating arguments, Acta Math. Appl. Sin., 15, 297-302, (1999) · Zbl 1020.34059 [20] Agarwal, R. P.; Berezansky, L.; Braverman, E.; Domoshnitsky, A., Non-oscillation theory of functional differential equations with applications, (2012), Springer New York, Dordrecht Heidelberg London [21] Erbe, L. H.; Kong, Q.; Zhang, B. G., Oscillation theory for functional differential equations, (1995), Dekker New York
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.