- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 405397, 8 pages
Oscillation Criteria of Third-Order Nonlinear Impulsive Differential Equations with Delay
School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, China
Received 14 November 2012; Accepted 10 January 2013
Academic Editor: Norio Yoshida
Copyright © 2013 Xiuxiang Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, 1993.
- G. Ballinger and X. Liu, “Existence, uniqueness and boundedness results for impulsive delay differential equations,” Applicable Analysis, vol. 74, no. 1-2, pp. 71–93, 2000.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, New Jersey, NJ, USA, 1989.
- A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14, World Scientific Publishing, New Jersey, NJ, USA, 1995.
- Y. S. Chen and W. Z. Feng, “Oscillations of second order nonlinear ODE with impulses,” Journal of Mathematical Analysis and Applications, vol. 210, no. 1, pp. 150–169, 1997.
- R. P. Agarwal, F. Karakoc, and A. Zafer, “A survey on oscillation of impulsive ordinary differential equations,” Advances in Differential Equations, vol. 2010, pp. 1–52, 2010.
- W.-H. Mao and A.-H. Wan, “Oscillatory and asymptotic behavior of solutions for nonlinear impulsive delay differential equations,” Acta Mathematicae Applicatae Sinica, vol. 22, English Series, no. 3, pp. 387–396, 2006.
- L. Erbe, A. Peterson, and S. H. Saker, “Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales,” Journal of Computational and Applied Mathematics, vol. 181, no. 1, pp. 92–102, 2005.
- L. Erbe, A. Peterson, and S. H. Saker, “Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation,” The Canadian Applied Mathematics Quarterly, vol. 14, no. 2, pp. 124–147, 2006.
- L. Erbe, A. Peterson, and S. H. Saker, “Hille and Nehari type criteria for third-order dynamic equations,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 112–131, 2007.
- S. H. Saker, “Oscillation criteria of third-order nonlinear delay differential equations,” Mathematica Slovaca, vol. 56, no. 4, pp. 433–450, 2006.
- S. H. Saker and J. Džurina, “On the oscillation of certain class of third-order nonlinear delay differential equations,” Mathematica Bohemica, vol. 135, no. 3, pp. 225–237, 2010.
- J. Yu and J. Yan, “Positive solutions and asymptotic behavior of delay differential equations with nonlinear impulses,” Journal of Mathematical Analysis and Applications, vol. 207, no. 2, pp. 388–396, 1997.
- T. Candan and R. S. Dahiya, “Oscillation of third order functional differential equations with delay,” in Proceedings of the 5th Mississippi State Conference on Differential Equations and Computational Simulations, vol. 10, p. 79, 2003.
- I. V. Kamenev, “An integral criterion for oscillation of linear differential equations of second order,” Matematicheskie Zametki, vol. 23, pp. 136–138, 1978.
- G. Ladas, Y. G. Sficas, and I. P. Stavroulakis, “Necessary and sufficient conditions for oscillations of higher order delay differential equations,” Transactions of the American Mathematical Society, vol. 285, no. 1, pp. 81–90, 1984.
- B. Baculíková, E. M. Elabbasy, S. H. Saker, and J. Džurina, “Oscillation criteria for third-order nonlinear differential equations,” Mathematica Slovaca, vol. 58, no. 2, pp. 201–220, 2008.