×
Liu, Xiuxiang

Oscillation criteria of third-order nonlinear impulsive differential equations with delay. (English) Zbl 1267.34064

Abstr. Appl. Anal. 2013, Article ID 405397, 8 p. (2013).
Summary: This paper deals with the oscillation of third-order nonlinear impulsive equations with delay. The results in this paper improve and extend some results for the equations without impulses. Some examples are given to illustrate the main results.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
PDFBibTeX XMLCite
\textit{X. Liu}, Abstr. Appl. Anal. 2013, Article ID 405397, 8 p. (2013; Zbl 1267.34064)
Full Text: DOI
OA License

References:

[1] Bainov, D. D.; Simeonov, P. S., Impulsive Differential Equations: Periodic Solutions and Applications (1993), Longman Scientific and Technical · Zbl 0815.34001
[2] Ballinger, G.; Liu, X., Existence, uniqueness and boundedness results for impulsive delay differential equations, Applicable Analysis, 74, 1-2, 71-93 (2000) · Zbl 1031.34081 · doi:10.1080/00036810008840804
[3] Lakshmikantham, V.; Baĭnov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations, 6 (1989), New Jersey, NJ, USA: World Scientific Publishing, New Jersey, NJ, USA · Zbl 0719.34002
[4] Samoĭlenko, A. M.; Perestyuk, N. A., Impulsive Differential Equations, 14 (1995), New Jersey, NJ, USA: World Scientific Publishing, New Jersey, NJ, USA · Zbl 0837.34003 · doi:10.1142/9789812798664
[5] Chen, Y. S.; Feng, W. Z., Oscillations of second order nonlinear ODE with impulses, Journal of Mathematical Analysis and Applications, 210, 1, 150-169 (1997) · Zbl 0877.34014 · doi:10.1006/jmaa.1997.5378
[6] Agarwal, R. P.; Karakoc, F.; Zafer, A., A survey on oscillation of impulsive ordinary differential equations, Advances in Differential Equations, 2010, 1-52 (2010) · Zbl 1193.34064 · doi:10.1155/2010/354841
[7] Mao, W.-H.; Wan, A.-H., Oscillatory and asymptotic behavior of solutions for nonlinear impulsive delay differential equations, Acta Mathematicae Applicatae Sinica, 22, 3, 387-396 (2006) · Zbl 1110.34058 · doi:10.1007/s10255-006-0313-8
[8] Erbe, L.; Peterson, A.; Saker, S. H., Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales, Journal of Computational and Applied Mathematics, 181, 1, 92-102 (2005) · Zbl 1075.39010 · doi:10.1016/j.cam.2004.11.021
[9] Erbe, L.; Peterson, A.; Saker, S. H., Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation, The Canadian Applied Mathematics Quarterly, 14, 2, 124-147 (2006) · Zbl 1145.34329
[10] Erbe, L.; Peterson, A.; Saker, S. H., Hille and Nehari type criteria for third-order dynamic equations, Journal of Mathematical Analysis and Applications, 329, 1, 112-131 (2007) · Zbl 1128.39009 · doi:10.1016/j.jmaa.2006.06.033
[11] Saker, S. H., Oscillation criteria of third-order nonlinear delay differential equations, Mathematica Slovaca, 56, 4, 433-450 (2006) · Zbl 1141.34040
[12] Saker, S. H.; Džurina, J., On the oscillation of certain class of third-order nonlinear delay differential equations, Mathematica Bohemica, 135, 3, 225-237 (2010) · Zbl 1224.34217
[13] Yu, J.; Yan, J., Positive solutions and asymptotic behavior of delay differential equations with nonlinear impulses, Journal of Mathematical Analysis and Applications, 207, 2, 388-396 (1997) · Zbl 0877.34054 · doi:10.1006/jmaa.1997.5276
[14] Candan, T.; Dahiya, R. S., Oscillation of third order functional differential equations with delay, Proceedings of the 5th Mississippi State Conference on Differential Equations and Computational Simulations · Zbl 1028.34061
[15] Kamenev, I. V., An integral criterion for oscillation of linear differential equations of second order, Matematicheskie Zametki, 23, 136-138 (1978) · Zbl 0408.34031
[16] Ladas, G.; Sficas, Y. G.; Stavroulakis, I. P., Necessary and sufficient conditions for oscillations of higher order delay differential equations, Transactions of the American Mathematical Society, 285, 1, 81-90 (1984) · Zbl 0528.34070 · doi:10.2307/1999473
[17] Baculíková, B.; Elabbasy, E. M.; Saker, S. H.; Džurina, J., Oscillation criteria for third-order nonlinear differential equations, Mathematica Slovaca, 58, 2, 201-220 (2008) · Zbl 1174.34052 · doi:10.2478/s12175-008-0068-1
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.