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Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform

  • Gunasekaran Nithyakala , Govindasamy Ayyappan , Jehad Alzabut EMAIL logo and Ethiraju Thandapani
Published/Copyright: May 13, 2024
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 74 Issue 1

Abstract

In the present paper, new oscillation criteria are established for fourth-order delay differential equations of the form

(a3(t)(a2(t)a1(t)x′(t)′)′)′+b(t)xα(σ(t))=0

under the assumption (noncanonical)

∫t0∞1aj(t)dt<∞,j=1, 2, 3.

We convert the equation into a canonical type, utilize the comparison method, and the Riccati transformation to find sufficient conditions for oscillation of all solutions to the aforementioned problem. This approach greatly simplifies the examination analysis, and provides a substantial improvement of the current results and this is documented by several evidences and illustrated by numerical examples.

Keywords: Delay differential equation; non-canonical; fourth-order; oscillation
MSC 2010: Primary 34C10; Secondary 34K11

J. Alzabut is thankful to Prince Sultan University and OSTİM Technical University for their endless support.

  1. (Communicated by Michal Fečkan)

References

[1] Agarwal, R. P.—Grace, S. R.—Manojlovic, J. V.: Oscillation criteria for certain fourth order nonlinear functional differential equations, Math. Comput. Model. 44 (2006), 163–187.Search in Google Scholar

[2] Baculíková, B.—Džurina, J.: The fourth order strongly noncanonical operators, Open Math. 16 (2018), 1667–1674.Search in Google Scholar

[3] BartuŠek, M.—DoŠlá, Z.: Asymptotic problems for fourth-order nonlinear differential equations, Bound. Value Probl. 2013 (2013), Art. No. 89.Search in Google Scholar

[4] Bazighifan, O.: Oscillatory behavior of fourth-order differential equations with delay argument, Palest. J. Math. 9 (2020), 569–578.Search in Google Scholar

[5] El-Nabulsi, R. A.—Moaaz, O.—Bazighifan, O.: New results for oscillatory behavior of fourth-order differential equations, Symmetry 12 (2020), Art. No. 136.Search in Google Scholar

[6] Esmailzadeh, E.—Ghorashi, M.: Vibration analysis of beams traversed by uniform partially distributed moving masses, J. Sound Vib. 184 (1995), 9–17.Search in Google Scholar

[7] Grace, S. R.—Agarwal, R. P.—Graef, J. R.: Oscillation thorems for fourth-order functional differential equations, J. Appl. Math. Comput. 30 (2009), 75–88.Search in Google Scholar

[8] Grace, S. R.—Bohner, M.—Liu, A.: Oscillation criteria for fourth-order functional differential equations, Math. Slovaca 63 (2013), 1303–1320.Search in Google Scholar

[9] Grace, S. R.—Džurina, J.—Jadlovská, I.—LI, T.: On the oscillation of fourth-order delay differential equations, Adv. Difference Equ. 2019 (2019), Art. No. 118.Search in Google Scholar

[10] JaroŠ, J.—TAKASI, K.—TANIGAWA, T.: Oscillation criteria for fourth-order half-linear differential equations, Arch. Math. (Brno) 56 (2020), 115–125.Search in Google Scholar

[11] Kiguradze, I. T.—Chauturia, T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Kluwer Acad. Dordrecht, 1993.Search in Google Scholar

[12] Kitamura, Y.—Kusano, T.: Oscillation of first order nonlinear differential equations with deviating arguments, Proc. Amer. Math. Soc. 78 (1980), 64–68.Search in Google Scholar

[13] Ladde, G. S.—Lakshmikantham, V.—ZHANG, B. G.: Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York, 1987.Search in Google Scholar

[14] Moaaz, O.—Kumam, P.—Bazighifan, O.: On the oscillatory behavior of a class of fourth-order nonlinear differential equation, Symmetry 12 (2020), Art. No. 524.Search in Google Scholar

[15] Philos, Ch. G.: On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays, Arch. Math. 36 (1981), 168–178.Search in Google Scholar

[16] Sakamoto, T.—Tanaka, S.: Eventually positive solutions of first order nonlinear differential equations with a deviating argument, Acta Math. Hungar. 127 (2010), 17–33.Search in Google Scholar

[17] Zhang, C. H.—Li, T.—Thandapani, E.: Asymptotic behavior of fourth-order neutral dynamic equations with non-canonical operators, Taiwanese J. Math. 18 (2014), 1003–1019.Search in Google Scholar
Received: 2023-03-08
Accepted: 2023-05-15
Published Online: 2024-05-13
Published in Print: 2024-02-26

© 2024 Mathematical Institute Slovak Academy of Sciences

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  8. Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
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  15. Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
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https://doi.org/10.1515/ms-2024-0008
Keywords for this article
Delay differential equation; non-canonical; fourth-order; oscillation

Articles in the same Issue

  1. Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
  2. On hyper (r, q)-Fibonacci polynomials
  3. The pointfree version of 𝓒c(X) via the ranges of functions
  4. On the x-coordinates of Pell equations that are products of two Pell numbers
  5. Subordination properties and coefficient problems for a novel class of convex functions
  6. Certain radii problems for 𝓢∗(ψ) and special functions
  7. On direct and inverse Poletsky inequalities with a tangential dilatation
  8. Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
  9. Hermite interpolation of type total degree associated with certain spaces of polynomials
  10. Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
  11. A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
  12. Compact subsets of Cλ,u(X)
  13. Variations of star selection principles on hyperspaces
  14. On lower density operators
  15. Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
  16. On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
  17. Large deviations for some dependent heavy tailed random sequences
  18. Metric, stratifiable and uniform spaces of G-permutation degree
  19. In memory of Paolo
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