Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations
Abstract
:1. Introduction
- (H1).
- , , , , ;
- (H2).
- .
2. Main Results
2.1. Equation (1) Satisfies Condition (2)
2.2. Equation (1) Satisfies Condition (3)
3. Example
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Fowler, R.H. Further studies of Emden’s and similar differential equations. Q. J. Math. 1931, 2, 259–288. [Google Scholar] [CrossRef]
- Berkovich, L.M. The generalized Emden-Fowler equation. Symmtry Nonlinear Math. Phys. 1997, 1, 155–163. [Google Scholar]
- Hale, J.K. Theory of Functional Differential Equations; Springer: New York, NY, USA, 1977. [Google Scholar]
- Muhib, A.; Alotaibi, H.; Bazighifan, O.; Nonlaopon, K. Oscillation theorems of solution of second-order neutral differential equations. AIMS Math. 2021, 6, 12771–12779. [Google Scholar] [CrossRef]
- Wong, J.S.W. On the generalized emden-fowler equation. SIAM Rev. 1975, 17, 339–360. [Google Scholar] [CrossRef]
- Li, T.X.; Frassu, S.; Viglialoro, G. Combining effects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption. Z. Angew. Math. Phys. 2023, 74, 109. [Google Scholar] [CrossRef]
- Li, T.X.; Pintus, N.; Viglialoro, G. Properties of solutions to porous medium problems with different sources and boundary conditions. Z. Angew. Math. Phys. 2019, 70, 86. [Google Scholar] [CrossRef]
- Li, T.X.; Viglialoro, G. Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime. Differ. Integral Equ. 2021, 34, 315–336. [Google Scholar] [CrossRef]
- Agarwal, R.P.; Bohner, M.; Li, T.X.; Zhang, C.H. Oscillation of second-order Emden-Fowler neutral delay differential equations. Ann. Mat. Pura Appl. 2014, 193, 1861–1875. [Google Scholar] [CrossRef]
- Abdelnaser, A.; Moaaz, O.; Cesarano, C.; Askar, S.; Elabbasy, E.M. Oscillation Test for Second-Order Differential Equations with Several Delays. Symmetry 2023, 15, 452. [Google Scholar] [CrossRef]
- Agarwal, R.P.; Zhang, C.H.; Li, T.X. Some remarks on oscillation of second order neutral differential equations. Appl. Math. Comput. 2016, 274, 178–181. [Google Scholar] [CrossRef]
- Baculíková, B. Oscillation of second order half-linear differential equations with deviating arguments of mixed type. Appl. Math. Lett. 2021, 119, 107228. [Google Scholar] [CrossRef]
- Baculíková, B.; Džurina, J. Oscillation theorems for second-order nonlinear neutral differential equations. Comput. Math. Appl. 2011, 62, 4472–4478. [Google Scholar] [CrossRef]
- Baculíková, B.; Džurina, J. New asymptotic results for half-linear differential equations with deviating argument. Carpathian J. Math. 2022, 38, 327–335. [Google Scholar] [CrossRef]
- Džurina, J.; Grace, S.R.; Jadlovsk, I.; Li, T.X. Oscillation criteria for second-order Emden-Fowler delay differenrial equations with a sublinear neutral term. Math. Nachr. 2020, 293, 910–922. [Google Scholar] [CrossRef]
- Feng, L.M.; Sun, S.R. Oscillation of second-order Emden-Fowler neutral differential equations with advanced and delay arguments. Bull. Malays. Math. Sci. Soc. 2020, 43, 3777–3790. [Google Scholar] [CrossRef]
- Grace, S.R.; Džurina, J.; Jadlovsk, I.; Li, T.X. An improved approach for studying oscillation of second-order neutral delay differential equations. J. Ineuqal. Appl. 2018, 2018, 193. [Google Scholar] [CrossRef] [PubMed]
- Hindi, A.A.; Moaaz, O.; Cesarano, C.; Alharbi, W.; Abdou, M.A. Noncanonical Neutral DDEs of Second-Order: New Sufficient Conditions for Oscillation. Mathematics 2021, 9, 2026. [Google Scholar] [CrossRef]
- Hassan, T.S.; Moaaz, O.; Nabih, A.; Mesmouli, M.B.; El-Sayed, A.M.A. New Sufficient Conditions for Oscillation of Second-Order Neutral Delay Differential Equations. Axioms 2021, 10, 281. [Google Scholar] [CrossRef]
- Jadlovská, I. New criteria for sharp oscillation of second-order neutral delay differential equations. Mathematics 2021, 9, 2089. [Google Scholar] [CrossRef]
- Li, T.X.; Han, Z.L.; Zhang, C.H.; Sun, S.R. On the oscillation of second-order Emden-Fowler neutral differential equations. J. Appl. Math. Comput. 2011, 37, 601–610. [Google Scholar] [CrossRef]
- Li, T.X.; Rogovchenko, Y.V. Oscillation of second-order neutral differential equations. Math. Nachr. 2015, 10, 1150–1162. [Google Scholar] [CrossRef]
- Li, T.X.; Rogovchenko, Y.V. Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations. Monatsh. Math. 2017, 184, 489–500. [Google Scholar] [CrossRef]
- Li, T.X.; Rogovchenko, Y.V. On asymptotic behavior of solutions to higher-order sublinear Emden-Fowler delay differential equations. Appl. Math. Lett. 2017, 67, 53–59. [Google Scholar] [CrossRef]
- Moaaz, O.; Elabbasy, E.M.; Qaraad, B. An improved approach for studying oscillation of generalized Emden-Fowler neutral differential equation. J. Ineuqal. Appl. 2020, 2020, 69. [Google Scholar] [CrossRef]
- Moaaz, O.; Ramos, H.; Awrejcewicz, J. Second-order Emden-Fowler neutral differential equations: A new precise criterion for oscillation. Appl. Math. Lett. 2021, 118, 107172. [Google Scholar] [CrossRef]
- Wu, Y.Z.; Yu, Y.H.; Xiao, J.S. Oscillation of second-order Emden-Fowler neutral delay differential equations. Electron. J. Differ. Equ. 2018, 2018, 1–15. [Google Scholar]
- Wu, Y.Z.; Yu, Y.H.; Zhang, J.M.; Xiao, J.S. Oscillation criteria for second-order Emden-Fowler functional differential equations of neutral type. J. Ineuqal. Appl. 2016, 2016, 328. [Google Scholar] [CrossRef]
- Zeng, Y.H.; Luo, L.P.; Yu, Y.H. Oscillation for Emden-Fowler delay differential equations of neutral type. Acta Math. Sci. Ser. A (Chin. Ed.) 2015, 35, 803–814. [Google Scholar]
- Zhang, S.-Y.; Wang, Q.-R. Oscillation of second-order nonlinear neutral dynamic equations on time scales. Appl. Math. Comput. 2010, 216, 2837–2848. [Google Scholar] [CrossRef]
- Li, T.X.; Rogovchenko, Y.V. Oscillation criteria for even-order neutral differential equations. Appl. Math. Lett. 2016, 61, 35–41. [Google Scholar] [CrossRef]
- Li, T.X.; Rogovchenko, Y.V. On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Appl. Math. Lett. 2020, 105, 106293. [Google Scholar] [CrossRef]
- Chatzarakis, G.E.; Grace, S.R.; Jadlovská, I.; Li, T.X.; Tunç, E. Oscillation criteria for third-order Emden-Fowler differential equations with unbounded neutral coefficients. Complexity 2019, 2019, 5691758. [Google Scholar] [CrossRef]
- Kiguradze, I.; Chanturia, T. Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Mathematics and Its Applications; Kluwer Academic Publishers Group: Dordrecht, The Netherlands, 1993. [Google Scholar]
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Tian, H.; Guo, R. Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations. Mathematics 2024, 12, 1559. https://doi.org/10.3390/math12101559
Tian H, Guo R. Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations. Mathematics. 2024; 12(10):1559. https://doi.org/10.3390/math12101559
Chicago/Turabian StyleTian, Haifeng, and Rongrong Guo. 2024. "Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations" Mathematics 12, no. 10: 1559. https://doi.org/10.3390/math12101559