Oscillation of noncanonical second-order advanced differential equations via canonical transform

Year 2022, , 7 - 13, 14.03.2022

Martin Bohner , Kumar S. Vıdhyaa Ethiraju Thandapani

https://doi.org/10.33205/cma.1055356

Cited By: 8

Abstract

In this paper, we develop a new technique to deduce oscillation of a second-order noncanonical advanced differential equation by using established criteria for second-order canonical advanced differential equations. We illustrate our results by presenting two examples.

Keywords

Advanced differential equation, canonical transform, second-order, oscillation

References

• R. P. Agarwal, M. Bohner andW. T. Li: Nonoscillation and oscillation: theory for functional differential equations, volume 267 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 2004.
• R. P. Agarwal, S. R. Grace and D. O’Regan: Oscillation theory for second order linear, halflinear, superlinear and sublinear dynamic equations, Kluwer Academic Publishers, Dordrecht, 2002.
• R. P. Agarwal, C. Zhang and T. Li: New Kamenev-type oscillation criteria for second-order nonlinear advanced dynamic equations, Appl. Math. Comput., 225 (2013), 822–828.
• B. Baculíková: Oscillation of second-order nonlinear noncanonical differential equations with deviating argument, Appl. Math. Lett., 91 (2019), 68–75.
• G. E. Chatzarakis, J. Džurina and I. Jadlovská: New oscillation criteria for second-order half-linear advanced differential equations, Appl. Math. Comput., 347 (2019), 404–416.
• G. E. Chatzarakis, S. R. Grace and I. Jadlovská: A sharp oscillation criterion for second-order half-linear advanced differential equations, Acta Math. Hungar., 163 (2) (2021), 552–562.
• G. E. Chatzarakis, I. Jadlovská: Improved oscillation results for second-order half-linear delay differential equations, Hacet. J. Math. Stat., 48 (1) (2019) 170–179.
• G. Chatzarakis, O. Moaaz, T. Li and B. Qaraad: Some oscillation theorems for nonlinear secondorder differential equations with an advanced argument, Adv. Difference Equ., Paper No. 160 (2020), 17 pages.
• J. Džurina: Oscillation of second order differential equations with advanced argument, Math. Slovaca, 45 (3) (1995), 263–268.
• J. Džurina: Oscillation of second order advanced differential equations, Electron. J. Qual. Theory Differ. Equ., Paper No. 20 (2018), 9 pages.
• J. Džurina, S. R. Grace, I. Jadlovská and T. Li: Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293 (5) (2020), 910–922.
• J. Džurina, I. Jadlovská: A sharp oscillation result for second-order half-linear noncanonical delay differential equations Electron. J. Qual. Theory Differ. Equ., Paper No. 46 (2020), 14 pages.
• J. Džurina, I. P. Stavroulakis: Oscillation criteria for second-order delay differential equations, Appl. Math. Comput., 140 (2-3) (2003), 445–453.
• J. R. Graef: Oscillation of higher order functional differential equations with an advanced argument, Appl. Math. Lett., 111 (2021), Paper No. 106685, 6.
• I. Gy˝ori, G. Ladas: Oscillation theory of delay differential equations. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1991.With applications, Oxford Science Publications.
• I. Jadlovská: Oscillation criteria of Kneser-type for second-order half-linear advanced differential equations. Appl. Math. Lett., 106 (2020), 106354, 8.
• N. Kılıç, Ö. Öcalan, and U. M. Özkan: Oscillation tests for nonlinear differential equations with several nonmonotone advanced arguments, Appl. Math. E-Notes, 21 (2021), 253–262.
• T. Kusano, M. Naito: Comparison theorems for functional-differential equations with deviating arguments. J. Math. Soc. Japan, 33 (3) (1981), 509–532.
• T. Li, Y. V. Rogovchenko: Oscillation of second-order neutral differential equations, Math. Nachr., 288 (10) (2015), 1150–1162.
• T. Li, Y. V. Rogovchenko: Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math., 184 (3) (2017), 489–500.
• T. Li, Y. V. Rogovchenko: On the asymptotic behavior of solutions to a class of third-order non-linear neutral differential equations, Appl. Math. Lett., 105 (2020), 106293, 7.
• A. M. Pedro: Oscillatory behavior of linear mixed-type systems, Rend. Circ. Mat. Palermo (2), 2021. doi: 10.1007/s12215-021-00658-y
• S. Tang, T. Li, R. P. Agarwal and Martin Bohner: Oscillation of odd-order half-linear advanced differential equations, Commun. Appl. Anal., 16 (3) (2012), 349–357.
• C. Vetro, D.Wardowski: Asymptotics for third-order nonlinear differential equations: Nonoscillatory and oscillatory cases, Asymptot. Anal., (2021), 1–19. doi:10.3233/ASY-211710