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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 4

Some new oscillation criteria for second-order hybrid differential equations

G. E. Chatzarakis(School of Pedagogical and Technological Education (ASPETE))0000-0002-0477-1895
M. Deepa(Thiruvalluvar Government Arts College)0000-0001-6210-4911
N. Nagajothi(Thiruvalluvar Government Arts College)0000-0002-3635-2396
V Sadhasivam(Thiruvalluvar Government Arts College)0000-0001-5333-0001
Pages
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Publication Date
2020-08-06
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We illustrate the validity of our results by means of various examples. *************************************************************************************

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider the second order hybrid differential equations.
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Key Findings & Data:For this class of equations, we establish a new criterion to check whether all solutions of an equation, in this class, oscillate.
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Conclusion & Impact:We illustrate the validity of our results by means of various examples. *************************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Oscillation · Hybrid Differential Equation · Riccati technique

Abstract

In this paper, we consider the second order hybrid differential equations. For this class of equations, we establish a new criterion to check whether all solutions of an equation, in this class, oscillate. We prove this criterion, using a generalized Riccati technique and an averaging method. The established oscillatory criteria have a distinct form, from all other relevant criteria, in the literature. We illustrate the validity of our results by means of various examples. *************************************************************************************

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Cite This Article

Chatzarakis, G. E., Deepa, M., Nagajothi, N., Sadhasivam, V. (2020). Some new oscillation criteria for second-order hybrid differential equations. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 4. https://doi.org/10.15672/hujms.541773

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References (27)

  1. H.Kh. Abdullah, Oscillation conditions of second-order nonlinear differential equations, Int. J. Math. Sci. 34 (1), 1490-1497, 2014.
  2. R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation theory for difference and differential equations, Kluwer academic publishers, Dordrecht, 2000.
  3. R.P. Agarwal and D. O’Regan, An introduction to ordinary differential equations, Springer, Newyork, 2008.
  4. B.C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid Syst. 4, 414-424, 2010.
  5. E.M. Elabbasy, T.S. Hassan and S.H. Saker, Oscillation of second-order nonlinear differential equations with a damping term, Electron. J. Differ. Eq. 76, 1-13, 2005.
  6. X. Fu, T. Li and C. Zhang, Oscillation of second-order damped differential equations, Adv. Difference Equ. 326, 2013.
  7. H. Ge and J. Xin, On the existence of a mild solution for impulsive hybrid fractional differential equations, Adv. Difference Equ. 211, 2013.
  8. S.R. Grace, Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl. 171, 220-241, 1992.
  9. M.A.E. Herzallah and D. Baleanu, On fractional order hybrid differential equations, Abstr. Appl. Anal. 2014, Article ID 389386, 2014.
  10. M. Heydari, G.B. Loghmani, S.M. Hosseini and S.M. Karbassi, Application of hybrid functions for solving diffing-harmonic oscillator, J. Difference Equ. 2014, Article ID 210754, 2014.
  11. W.G. Kelley and A.C. Peterson, The theory of differential equations: classical and qualitative, Springer, NewYork, 2010.
  12. H. Liu and F. Meng, Interval oscillation criteria for second-order nonlinear forced differential equations involving variable exponent, Adv. Difference Equ. 291, 2016.
  13. Z. Luo and J. Shen, Oscillation of second order linear differential equations with impulses, Appl. Math. Lett. 20, 75-81, 2007.
  14. K. Maleknejad and L. Torkzadeh, Application of hybrid functions for solving oscillator equations, Rom. Journ. Phys. 60 (1-2), 87-98, 2015.
  15. J.V. Manojlovic, Oscillation criteria for second-order half-linear differential equations, Math. Comput. Modelling 30, 109-119, 1999.
  16. P. Micheau and P. Coirault, A harmonic controller of engine speed oscillations for hybrid vehicles, Elsevier IFAC publications, 19-24, 2005.
  17. A.K. Nandakumaran, P.S. Datti and R.K. George, Ordinary differential equations, principles and applications, Cambridge University Press, 2017.
  18. A. Ozbekler, J.S.W. Wong, A. Safer, Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients, Appl. Math. Lett. 24, 1225-1230, 2011.
  19. Ch.G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math. 53, 482-492, 1989.
  20. V. Sadhasivam and M. Deepa, Oscillation criteria for fractional impulsive hybrid partial differential equations, Probl. Anal. Issues Anal. 8 (26), 73-91, 2019.
  21. S.H. Saker, Oscillation theory of delay differential and difference equations, VDM Verlag, Dr.Muller Aktiengesellschaft and Co, USA, 2010.
  22. S.H. Saker, P.Y.H. Pang and R.P. Agarwal, Oscillation theorems for second order nonlinear functional differential equations, Dynam. Systems Appl. 12, 307-322, 2003.
  23. S. Sitho, S.K. Ntouyas and J. Tariboon, Existence results for hybrid fractional integrodifferential equations, Bound. Value Probl. 113, 1-13, 2015.
  24. J.S.W. Wong, On Kamenev-type oscillation Theorems for second-order differential equations with damping, J. Math. Anal. Appl. 258, 244-257, 2001.
  25. F. Yuan and D. DiClemente, Hybrid voltage-controlled oscillator with low phase noise andlarge frequency tunig range, Analog Integr Circ Sig Process 82, 471-478, 2015.
  26. Y. Zhao, S. Sun, Z. Han and Q. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl. 62, 1312-1324, 2011.
  27. A. Zhao, Y. Wang and J. Yan, Oscillation criteria for second-order nonlinear differential equations with nonlinear damping, Comput. Math. Appl. 56, 542-555, 2008.