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Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales

Yıl 2022, , 273 - 278, 30.09.2022
https://doi.org/10.53006/rna.1075859

Öz

The notion of third order semicanonical dynamic equations on time scales is introduced so that any third order equation is either in canonical, noncanonical, or semicanonical form. Then a technique for transforming each of the two types of semicanonical equations to an equation in canonical form is given. The end result is that oscillation and other asymptotic results for canonical equations can then be applied to obtain analogous results for semicanonical equations.

Kaynakça

  • [1] B. Baculíková, J. Dzurina, and I. Jadlovská, On asymptotic properties of solutions to third-order delay differential equations, Electron. J. Qual. Theory Differ. Eqs. 2019 (2019), No. 7, 1-11.
  • [2] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
  • [3] M. Bohner, K.S. Vidhyaa, and E. Thandapani, Oscillation of noncanonical second-order advanced differential equations via canonical transform, Constr. Math. Anal. 5 (2022), 7-13.
  • [4] G.E. Chatzarakis, J. Dzurina, and I. Jadlovská, Oscillatory and asymptotic properties of third-order quasilinear delay di?erential equations, J. Inequalities Applications 2019 (2019), No. 23.
  • [5] J. Dzurina, Oscillation of second order advanced di?erential equations, Electron. J. Qual. Theory Differ. Equ., 2018 (2018), No. 20, 9 pp.
  • [6] J. Dzurina and I. Jadlovská, Oscillation of third-order differential equations with noncanonical operators, Appl. Math. Comput. 336 (2018), 394-402.
  • [7] L. Erbe, T.S. Hassan, and A. Peterson, Oscillation of third order nonlinear functional dynamic equations on time scales, Di?er. Equ. Dyn. Syst. 18 (2010), 199-227.
  • [8] T.S. Hassan and Q. Kong, Asymptotic behavior of third order functional dynamic equations with γ-Laplacian and nonlinearities given by Riemann-Stieltjes integrals, Electron. J. Qual. Theory Differ. Equ. 2014 (2014), No. 40, 21 pp.
  • [9] R. Srinivasan, J.R. Graef, and E. Thandapani, Asymptotic behavior of semi-canonical third-order functional difference equations, J. Di?erence Equ. Appl. 28 (2022), 547-560.
  • [10] W.F. Trench, Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc. 189 (1974), 319-327.
Yıl 2022, , 273 - 278, 30.09.2022
https://doi.org/10.53006/rna.1075859

Öz

Kaynakça

  • [1] B. Baculíková, J. Dzurina, and I. Jadlovská, On asymptotic properties of solutions to third-order delay differential equations, Electron. J. Qual. Theory Differ. Eqs. 2019 (2019), No. 7, 1-11.
  • [2] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
  • [3] M. Bohner, K.S. Vidhyaa, and E. Thandapani, Oscillation of noncanonical second-order advanced differential equations via canonical transform, Constr. Math. Anal. 5 (2022), 7-13.
  • [4] G.E. Chatzarakis, J. Dzurina, and I. Jadlovská, Oscillatory and asymptotic properties of third-order quasilinear delay di?erential equations, J. Inequalities Applications 2019 (2019), No. 23.
  • [5] J. Dzurina, Oscillation of second order advanced di?erential equations, Electron. J. Qual. Theory Differ. Equ., 2018 (2018), No. 20, 9 pp.
  • [6] J. Dzurina and I. Jadlovská, Oscillation of third-order differential equations with noncanonical operators, Appl. Math. Comput. 336 (2018), 394-402.
  • [7] L. Erbe, T.S. Hassan, and A. Peterson, Oscillation of third order nonlinear functional dynamic equations on time scales, Di?er. Equ. Dyn. Syst. 18 (2010), 199-227.
  • [8] T.S. Hassan and Q. Kong, Asymptotic behavior of third order functional dynamic equations with γ-Laplacian and nonlinearities given by Riemann-Stieltjes integrals, Electron. J. Qual. Theory Differ. Equ. 2014 (2014), No. 40, 21 pp.
  • [9] R. Srinivasan, J.R. Graef, and E. Thandapani, Asymptotic behavior of semi-canonical third-order functional difference equations, J. Di?erence Equ. Appl. 28 (2022), 547-560.
  • [10] W.F. Trench, Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc. 189 (1974), 319-327.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

John R. Graef

Yayımlanma Tarihi 30 Eylül 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Graef, J. R. (2022). Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales. Results in Nonlinear Analysis, 5(3), 273-278. https://doi.org/10.53006/rna.1075859
AMA Graef JR. Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales. RNA. Eylül 2022;5(3):273-278. doi:10.53006/rna.1075859
Chicago Graef, John R. “Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales”. Results in Nonlinear Analysis 5, sy. 3 (Eylül 2022): 273-78. https://doi.org/10.53006/rna.1075859.
EndNote Graef JR (01 Eylül 2022) Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales. Results in Nonlinear Analysis 5 3 273–278.
IEEE J. R. Graef, “Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales”, RNA, c. 5, sy. 3, ss. 273–278, 2022, doi: 10.53006/rna.1075859.
ISNAD Graef, John R. “Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales”. Results in Nonlinear Analysis 5/3 (Eylül 2022), 273-278. https://doi.org/10.53006/rna.1075859.
JAMA Graef JR. Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales. RNA. 2022;5:273–278.
MLA Graef, John R. “Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales”. Results in Nonlinear Analysis, c. 5, sy. 3, 2022, ss. 273-8, doi:10.53006/rna.1075859.
Vancouver Graef JR. Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales. RNA. 2022;5(3):273-8.