Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay
Abstract
:1. Introduction
- H1:
- and are quotients of odd positive integers and
- H2:
- and
- H3:
- and is not identically zero for large t;
- H4:
- and
2. Main Results
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Hale, J.K. Theory of Functional Differential Equations; Springer: New York, NY, USA, 1977. [Google Scholar]
- Agarwal, R.P.; Bohner, M.; Li, T.; Zhang, C. A new approach in the study of oscillatory behavior of even-order neutral delay diferential equations. Appl. Math. Comput. 2013, 225, 787–794. [Google Scholar]
- Agarwal, R.; Grace, S.; O’Regan, D. Oscillation Theory for Difference and Functional Differential Equations; Kluwer Acad. Publ.: Dordrecht, The Netherlands, 2000. [Google Scholar]
- Baculikova, B.; Dzurina, J. Oscillation theorems for second-order nonlinear neutral differential equations. Comput. Math. Appl. 2011, 62, 4472–4478. [Google Scholar] [CrossRef] [Green Version]
- Bazighifan, O.; Cesarano, C. Some New Oscillation Criteria for Second-Order Neutral Differential Equations with Delayed Arguments. Mathematics 2019, 7, 619. [Google Scholar] [CrossRef] [Green Version]
- Bazighifan, O.; Elabbasy, E.M.; Moaaz, O. Oscillation of higher-order differential equations with distributed delay. J. Inequal. Appl. 2019, 55, 1–9. [Google Scholar] [CrossRef] [Green Version]
- Chatzarakis, G.E.; Elabbasy, E.M.; Bazighifan, O. An oscillation criterion in 4th-order neutral differential equations with a continuously distributed delay. Adv. Differ. Equ. 2019, 2019, 336. [Google Scholar] [CrossRef]
- Chatzarakis, G.E.; Jadlovska, I.; Li, T. Oscillations of differential equations with non-monotone deviating arguments. Adv. Differ. Equ. 2019, 2019, 1–20. [Google Scholar] [CrossRef] [Green Version]
- Chatzarakis, G.E.; Li, T. Oscillations of differential equations generated by several deviating arguments. Adv. Differ. Equ. 2017, 2017, 292. [Google Scholar] [CrossRef]
- Chatzarakis, G.E.; Li, T. Oscillation criteria for delay and advanced differential equations with nonmonotone arguments. Complexity 2018, 2018, 8237634. [Google Scholar] [CrossRef] [Green Version]
- El-Nabulsi, R.A.; Moaaz, O.; Bazighifan, O. New Results for Oscillatory Behavior of Fourth-Order Differential Equations. Symmetry 2020, 12, 136. [Google Scholar] [CrossRef] [Green Version]
- Elabbasy, E.M.; Cesarano, C.; Bazighifan, O.; Moaaz, O. Asymptotic and oscillatory behavior of solutions of a class of higher order differential equation. Symmetry 2019, 11, 1434. [Google Scholar] [CrossRef] [Green Version]
- Elabbasy, E.M.; Hassan, T.S.; Moaaz, O. Oscillation behavior of second-order nonlinear neutral differential equations with deviating arguments. Opuscula Math. 2012, 32, 719–730. [Google Scholar] [CrossRef]
- Li, T.; Han, Z.; Zhao, P.; Sun, S. Oscillation of even-order neutral delay differential equations. Adv. Differ. Equ. 2010, 2010, 1–9. [Google Scholar] [CrossRef]
- Kiguradze, I.T.; Chanturiya, T.A. Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations; Kluwer Acad. Publ.: Dordrecht, The Netherlands, 1993. [Google Scholar]
- Moaaz, O. New criteria for oscillation of nonlinear neutral differential equations. Adv. Differ. Equ. 2019, 2019, 484. [Google Scholar] [CrossRef] [Green Version]
- Moaaz, O.; Elabbasy, E.M.; Bazighifan, O. On the asymptotic behavior of fourth-order functional differential equations. Adv. Differ. Equ. 2017, 2017, 261. [Google Scholar] [CrossRef] [Green Version]
- Moaaz, O.; Awrejcewicz, J.; Bazighifan, O. A New Approach in the Study of Oscillation Criteria of Even-Order Neutral Differential Equations. Mathematics 2020, 8, 197. [Google Scholar] [CrossRef] [Green Version]
- Moaaz, O.; Elabbasy, E.M.; Muhib, A. Oscillation criteria for even-order neutral differential equations with distributed deviating arguments. Adv. Differ. Equ. 2019, 2019, 297. [Google Scholar] [CrossRef] [Green Version]
- Moaaz, O.; Elabbasy, E.M.; Shaaban, E. Oscillation criteria for a class of third order damped differential equations. Arab. J. Math. Sci. 2018, 24, 16–30. [Google Scholar] [CrossRef]
- Park, C.; Moaaz, O.; Bazighifan, O. Oscillation Results for Higher Order Differential Equations. Axioms 2020, 9, 14. [Google Scholar] [CrossRef] [Green Version]
- Xing, G.; Li, T.; Zhang, C. Oscillation of higher-order quasi linear neutral differential equations. Adv. Differ. Equ. 2011, 2011, 45. [Google Scholar] [CrossRef] [Green Version]
- Zafer, A. Oscillation criteria for even order neutral differential equations. Appl. Math. Lett. 1998, 11, 21–25. [Google Scholar] [CrossRef] [Green Version]
- Zhang, Q.; Yan, J. Oscillation behavior of even order neutral differential equations with variable coefficients. Appl. Math. Lett. 2006, 19, 1202–1206. [Google Scholar] [CrossRef] [Green Version]
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Moaaz, O.; El-Nabulsi, R.A.; Bazighifan, O. Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay. Symmetry 2020, 12, 371. https://doi.org/10.3390/sym12030371
Moaaz O, El-Nabulsi RA, Bazighifan O. Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay. Symmetry. 2020; 12(3):371. https://doi.org/10.3390/sym12030371
Chicago/Turabian StyleMoaaz, Osama, Rami Ahmad El-Nabulsi, and Omar Bazighifan. 2020. "Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay" Symmetry 12, no. 3: 371. https://doi.org/10.3390/sym12030371
APA StyleMoaaz, O., El-Nabulsi, R. A., & Bazighifan, O. (2020). Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay. Symmetry, 12(3), 371. https://doi.org/10.3390/sym12030371