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Oscillation of first-order delay differential equations

Published online by Cambridge University Press:  17 February 2009

Aimin Zhao ,
Xianhua Tang  and
Jurang Yan
Aimin Zhao
Affiliation:
Department of Mathematics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China.
Xianhua Tang
Affiliation:
Department of Applied Mathematics, Zhongnan University, Changsha, Hunan 410081, People's Republic of China.
Jurang Yan
Affiliation:
Department of Mathematics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China.
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Abstract

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This paper is concerned with the oscillation of first-order delay differential equations

where p(t) and τ(t) are piecewise continuous and nonnegative functions and τ(t) is non-decreasing. A new oscillation criterion is obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 4 , April 2004 , pp. 593 - 599
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Elbert, A. and Stavroulakis, I. P., “Oscillations of first order differential equations with deviating arguments”, in Recent trends in differential equations, World Sci. Ser. Appl. Anal. 1, (World Scientific, Singapore, 1992) 163–178.Google Scholar
[2]Elbert, A. and Stavroulakis, I. P., “Oscillation and non-oscillation criteria for delay differential equations”, Proc. Amer. Math. Soc. 13 (1995) 1503–1510.CrossRefGoogle Scholar
[3]Erbe, L. H. and Kong, Q., “Oscillation and nonoscillation properties of neutral differential equations”, Canad. J. Math. 46 (1994) 284–297.CrossRefGoogle Scholar
[4]Erbe, L. H. and Zhang, B. G., “Oscillation for first order linear differential equations with deviating arguments”, Diff. Integral Equations 1 (1988) 305–314.Google Scholar
[5]Gyori, I. and Ladas, G., Oscillation theory of delay differentia1 equations with applications (Clarendon Press, Oxford, 1991).CrossRefGoogle Scholar
[6]Jaroš, J. and Stavroulakis, I. P., “Oscillation tests for delay equations”, Rocky Mountain J. Math. 29 (1999) 197–207.Google Scholar
[7]Jian, C., “On the oscillation of linear differential equations with deviating arguments”, Math. Practice Theory 1 (1991) 32–40 (Chinese).Google Scholar
[8]Kon, M., Sficas, Y. G. and Stavroulakis, I. P., “Oscillation criteria for delay equations”, Proc. Amer. Math. Soc. 128 (2000) 2989–2997.CrossRefGoogle Scholar
[9]Koplatadze, R. G. and Chanturija, T. A., “On oscillatory and monotonic solutions of first order differential equations with deviating arguments”, Diff. Uravnenija 18 (1982) 1463–1465, (Russian).Google Scholar
[10]Kozakiewicz, E., “Conditions for the absence of positive solutions on a first order differential inequality with a single delay”, Arch. Math. (Brno) 31 (1995) 291–297.Google Scholar
[11]Ladas, G., Lakshmikantham, V. and Papadakis, L. S., “Oscillations of higher-order retarded differential equations generated by the retarded arguments”, in Delay and functional differential equations and their applications, (Academic Press, New York, 1972) 219–231.CrossRefGoogle Scholar
[12]Li, B., “Oscillation of first order delay differential equations”, Proc. Amer. Math. Soc. 124 (1996) 3729–3737.CrossRefGoogle Scholar
[13]Li, B., “Multiple integral average conditions for oscillation of delay differential equations”, J. Math. Anal. Appl. 219 (1998) 165–178.CrossRefGoogle Scholar
[14]Philos, Ch. G. and Sficas, Y. G., “An oscillation criterion for first order linear delay differential equations”, Canad. Math. Bull. 41 (1998) 207–213.CrossRefGoogle Scholar
[15]Sficas, Y. G. and Stavroulakis, I. P., “Oscillation criteria for first order delay equations”, Technical Report No. 6, Univ. of Ioannina, Dept of Math., Dec 2001, to appear in Bull. London Math. Soc.Google Scholar
[16]Shen, J. H., Stavroulakis, I. P. and Tang, X. H., “Oscillation and nonoscillation criteria for delay equations”, to appear.Google Scholar
[17]Tang, X. H., “Oscillation properties of solutions for differential equations with unbounded delays”, J. Qufu Normal Univ. 23 (1997) 38–44 (Chinese).Google Scholar
[18]Yu, J. S. and Wang, Z. C., “Some further results on oscillation of neutral differential equations”, Bull. Austral. Math. Soc. 46 (1992) 149–157.Google Scholar