ASYMPTOTIC PROPERTIES OF KNESER SOLUTIONS TO THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS

Martin Bohner; John R. Graef; Irena Jadlovská

doi:10.11948/20210439

2022 Volume 12 Issue 5

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Martin Bohner, John R. Graef, Irena Jadlovská. ASYMPTOTIC PROPERTIES OF KNESER SOLUTIONS TO THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2024-2032. doi: 10.11948/20210439

Citation:

Martin Bohner, John R. Graef, Irena Jadlovská. ASYMPTOTIC PROPERTIES OF KNESER SOLUTIONS TO THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2024-2032. doi: 10.11948/20210439

ASYMPTOTIC PROPERTIES OF KNESER SOLUTIONS TO THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS

1.
Missouri University of Science and Technology, Department of Mathematics and Statistics, Rolla, Missouri 65409-0020, USA
2.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
3.
Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

Corresponding author: Email: john-graef@utc.edu (J. R. Graef)

Abstract

Abstract

The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established.
- Third-order differential equation /
- delay /
- linear /
- Kneser solution /
- oscillation
MSC: 34C10, 34K11

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References

[1]	M. Adıvar, E. Akın and R. Higgins, Oscillatory behavior of solutions of third-order delay and advanced dynamic equations, J. Inequal. Appl., 2014, 2014(1), 1–16. doi: 10.1186/1029-242X-2014-1 CrossRef Google Scholar
[2]	B. Baculíková and J. Džurina, Oscillation of third-order nonlinear differential equations, Appl. Math. Lett., 2011, 24(4), 466–470. doi: 10.1016/j.aml.2010.10.043 CrossRef Google Scholar
[3]	B. Baculíková and J. Džurina, Remark on properties of Kneser solutions for third-order neutral differential equations, Appl. Math. Lett., 2017, 63, 1–5. doi: 10.1016/j.aml.2016.07.005 CrossRef Google Scholar
[4]	L. Berezansky, A. Domoshnitsky and R. Koplatadze, Oscillation, nonoscillation, stability and asymptotic properties for second and higher order functional differential equations, 2020. Google Scholar
[5]	M. Bohner, S. R. Grace and I. Jadlovská, Oscillation criteria for third-order functional differential equations with damping, Electron. J. Differential Equations, 2016, 2016(215), 1–15. Google Scholar
[6]	A. Domoshnitsky, S. Shemesh, A. Sitkin et al., Stabilization of third-order differential equation by delay distributed feedback control, J. Inequal. Appl., 2018, 2018(1), 1–13. doi: 10.1186/s13660-017-1594-6 CrossRef Google Scholar
[7]	A. Domoshnitsky, I. Volinsky and A. Polonsky, Stabilization of third order differential equation by delay distributed feedback control with unbounded memory, Math. Slovaca, 2019, 69(5), 1165–1176. doi: 10.1515/ms-2017-0298 CrossRef Google Scholar
[8]	Z. Došlá and P. Liška, Comparison theorems for third-order neutral differential equations, Electron J. Differential Equations, 2016, 38, 1–13. Google Scholar
[9]	S. R. Grace, Oscillation criteria for third order nonlinear delay differential equations with damping, Opuscula Mathematica, 2015, 35(4), 485–497. doi: 10.7494/OpMath.2015.35.4.485 CrossRef Google Scholar
[10]	S. R. Grace, R. P. Agarwal, R. Pavani and E. Thandapani, On the oscillation of certain third order nonlinear functional differential equations, Appl. Math. Comput., 2008, 202(1), 102–112. doi: 10.1016/j.amc.2008.01.025 CrossRef Google Scholar
[11]	J. R. Graef, I. Jadlovská and E. Tunç, Sharp asymptotic results for third-order linear delay differential equations, J. Appl. Anal. Comput., 2021, 11(5), 2459–2472. Google Scholar
[12]	P. Hartman and A. Wintner, Linear differential and difference equations with monotone solutions, Amer. J. Math., 1953, 75(4), 731–743. doi: 10.2307/2372548 CrossRef Google Scholar
[13]	I. T. Kiguradze and T. A. Chanturia, Asymptotic properties of solutions of nonautonomous ordinary differential equations, 89 of Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1993. Translated from the 1985 Russian original. Google Scholar
[14]	S. Padhi and S. Pati, Theory of third-order differential equations, Springer, New Delhi, 2014. Google Scholar
[15]	S. Saker, Oscillation Theory of Delay Differential and Difference Equations: Second and Third Orders, LAP Lambert Academic Publishing, 2010. Google Scholar