SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

Oscillation of fourth-order dynamic equations

Martin BOHNER
Shurong SUN
Said R. GRACE
Pages
545–553
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Some conditions are presented that ensure that all bounded solutions of the equation are oscillatory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we shall reduce the problem of the oscillation of all solu- tions of certain nonlinear fourth-order dynamic equations to the prob- lem of oscillation of two second-order dynamic equations, which are discussed intensively in the literature.
📊
Key Findings & Data:Further oscillation criteria of fourth-order equations are given and proved using integration and Tay- lor’s formula on time scales.
💡
Conclusion & Impact:Some conditions are presented that ensure that all bounded solutions of the equation are oscillatory.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we shall reduce the problem of the oscillation of all solu- tions of certain nonlinear fourth-order dynamic equations to the prob- lem of oscillation of two second-order dynamic equations, which are discussed intensively in the literature. Further oscillation criteria of fourth-order equations are given and proved using integration and Tay- lor’s formula on time scales. Some conditions are presented that ensure that all bounded solutions of the equation are oscillatory.

🔖

Cite This Article

BOHNER, M., SUN, S., GRACE, S. R. (2022). Oscillation of fourth-order dynamic equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 545–553. https://ajindex.com/articles/530638

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. Agarwal, R. P., Bohner, M. and Grace, S.R. On the oscillation of second-order half-linear dynamic equations, J. Difference Equ. Appl. 15 (5), 451–460, 2009
  2. Agarwal, R. P., Bohner, M., Grace, S.R. and O’Regan, D. Discrete Oscillation Theory (Hindawi Publishing Corporation, 2005)
  3. Agarwal, R.P., Grace, S.R. and O’Regan D. Oscillation Theory for Difference and Functional Differential Equations (Kluwer Academic Publishers, Dordrecht, 2000)
  4. Agarwal,R.P., Grace, S.R. and O’Regan, D. Oscillation Theory for Second Order Linear,Half-Linear, Superlinear and Sublinear Dynamic Equations (Kluwer Academic Publishers,Dordrecht, 2002)
  5. Agarwal, R.P., Grace, S.R. and O’Regan D. Oscillation Theory for Second Order Dynamic Equations, (Volume 5, Series in Mathematical Analysis and Applications, Taylor and Francis Ltd., London, 2003)
  6. Agarwal, R. P., Grace, S.R. and Wong, P. J.Y. Oscillation of fourth order nonlinear difference equations, Int. J. Difference Equ. 2 (2), 123–137, 2007
  7. Atadzhanov, B.A. Sufficient conditions for oscillation and nonoscillation of fourth-order equations, Izv. Akad. Nauk Turkmen. SSR Ser. Fiz.-Tekhn. Khim. Geol. Nauk 4, 9–17, 1990
  8. Bohner, M. and Guseinov, G. Sh. Multiple Lebesgue integration on time scales, Adv. Difference Equ. 12, Art. ID 26391, 2006
  9. Bohner, M. and Lutz, D.A. Asymptotic expansion and analytic dynamic equations, ZAMM Z. Angew. Math. Mech. 86 (1), 37–45, 2006
  10. Bohner, M. and Peterson, A. Dynamic Equations on Time Scales: An Introduction with Applications (Birkh¨auser, Boston, 2001)
  11. Bohner, M. and Peterson, A. Advances in Dynamic Equations on Time Scales (Birkh¨auser,Boston, 2003)
  12. Bohner, M. and Saker, S.H. Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math., 34 (4), 1239–1254, 2004
  13. Chang, Y. Oscillation of certain fourth order difference equations, Acta Math. Appl. Sinica 23 (3), 466–471, 2000
  14. Elias, U. Oscillation Theory of Two-Term Differential Equations (Volume 396, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 1997)
  15. Erbe, L., Peterson, A. and ˇReh´ak, P. Comparison theorems for linear dynamic equations on time scales, J. Math. Anal. Appl. 275 (1), 418–438, 2002
  16. Feng, B. and Yu, Y. On the oscillation of the fourth order differential equations, Chinese Quart. J. Math., 12 (4), 1–10, 1997
  17. Hilger, S. Analysis on measure chains – a unified approach to continuous and discrete calc