Oscillation criteria for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term
DOI:
https://doi.org/10.58997/ejde.2023.45Abstract
We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to \(0\) or \(\infty\). Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works.
For more informaton see https://ejde.math.txstate.edu/Volumes/2023/45/abstr.html
References
R. P. Agarwal, M. Bohner, S.R. Grace, D. O'Regan; Discrete Oscillation Theory, Hindawi Publ. Corp., New York, 2005.
R. P. Agarwal, M. Bohner, T. Li, C. Zhang; Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math., 30, 1{6, 2014.
G. Ayyappan, G. Nithyakala; Oscillation of second-order nonlinear difference equation with superlinear neutral term, Malaya J. Matematik, 7, 366{377, 2019.
G. Ayyappan, G. Nithyakala; Some oscillation results for even-order delay difference equations with a sublinear neutral term, Abstr. Appl. Anal., 6 pp., 2018. (Article ID 2590158).
M. Bohner, H. A. El-Marshedy, S. R. Grace, I. Sager; Oscillation of second-order nonlinear difference equations with sublinear neutral term, Math. Murav. 23, 1{10, 2019.
M. Bohner, T. Li; Oscillation of second orderp Laplace dynamic equations with a nonpositive neutral coefficient , Appl. Math. Lett., 37(2014), 72-76.
E. Chandrasekaran, G. E. Chatzarakis, G. Palani, E. Thandapani; Oscillation criteria for advanced difference equations of second order, Appl. Math. Comput., 372 (124963), 6 pp., 2020.
G. E. Chatzarakis, R. KanagaSabapathi, S. Selvarangam, E. Thandapani; Oscillation is second-order damped difference equations with a superlinear neutral term, Adv. Math.: Sci. J., 9, 10969{10981, 2020.
A. Columbu, S. Frassu, G. Viglialoro; Re ned criteria toward boundedness in an attraction-repulsion chemotaxis system with nonlinear productions, Appl. Anal., (2023), 1-17, DOI:10.1080/00036811.223.2187789.
C. Dharuman, J. R. Graef, E. Thandapani, K.S. Vidhyaa; Oscillation of second-order difference equation with a sublinear neutral term, J. Math. Appl. 40, 59{67, 2017.
C. Dharuman, E. Thandapani; Oscillation of solutions of nonlinear difference equation with a super-linear neutral term, Nonauton. Dyn. Syst., 5, 52{58, 2018.
J. Dzurina, S. R. Grace, I. Jadlovska, T. Li; Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math.Naghr.,293(5) (2020), 910-922.
S. R. Grace, J. R. Graef; Oscillatory behaviour of second order nonlinear differential equations with a sublinear neutral term, Math. Model. Anal., 23, 217{226, 2018.
S. Grace, J. Alzabut, Oscillation results for nonlinear second order difference equations with mixed neutral terms, Adv. difference Equ., (8), 12 pp., 2020.
S. R. Grace, I. Jadlovska,d A. Zafer; On oscillation of second order delay differential equations with a sublinear neutral term, Mediterr, J. Math. 17 (116), 11 pp., 2020.
S. R. Grace, J. R. Graef; Oscillation theorems for second-order delay difference equations with superlinear neutral terms, Georgian Math. J. 28, 725{731, 2021.
S. R. Grace; New oscillation criteria of nonlinear second order delay difference equations, Mediterr. J. Math., 19 (166), 11 pp., 2022.
J. R. Graef, S. R. Grace, E. Tunc; Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term, Opuscula Math., 39, 39{47, 2019.
I. Gyori, G. Ladas; Oscillation theory of delay differential equations with applications, Clareuden Press, Oxford, 1991.
J. K. Hale; Functional differential Equations, Springer, Berlin,1977.
B. Kamaraj, R. Vasuki; Oscillation of second order difference equations with a superlinear neutral term, J. Adv. Math. Comput. Sci. 23, 1{10 , 2017.
R. Kanagasabapathi, S. Selvarangam, J. R. Graef, E. Thandapani; Oscillation results using linearization of quasilinear second-order delay difference equations, Mediterr. J. Math., 18 (248), 14 pp., 2021.
T. Li, S.Frassu, G. Viglisloro; Combining e ects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys., 74(3) (2023), Art.109.
W. T. Li, S.H. Sager; Oscillation of second-order sublinear neutral delay difference equations, Appl. Math. Comput. 146, 543{551, 2003.
T. Li, Yuriy V. Rogovchenko; Oscillation of second-order neutral differential equations, Math.Nachr., 288(10) (2015), 1150-1162.
S. Meharbanu, S. Nalini; Oscillation of second order difference equations with several superlinear neutral terms, Adv. differ. Equ. 345, 10 p., 2018.
G. Nithyakala, G. Ayyappan; Oscillation theorems for second-order nonlinear difference equations with advanced superlinear neutral term, J. Anal. 30 (4), 1475{1484, 2022.
F. A. Rihan; Delay differential Equations and Applications to Biology, Springer Nature, Singapore,2021.
S. H. Saker, A. K. Sethi, Osman Tunc, Jehad Alzabut; Riccati technique for oscillation of second order nonlinear neutral delay dynamic equations, J. Math.Comput. Sci., 29 (4), 387{398, 2023.
W.Soedel; Vibrations of Shells and Plates, Marcel Dekker, New York, 1991.
E. Thandapani, Z. Hiu, R. Arul, P.S. Raja; Oscillation and asymmetric behavior of second order difference equations with nonlinear neutral term, Appl. Math. E. Notes 4, 59{67, 2004.
M. K. Yildiz, H. Ogunmez; Oscillation results of higher order nonlinear neutral delay differences equations with a nonlinear neutral term, Hacet. J. Math. Stat. 43, 809{844, 2014.
Z. Zhang, J. Chen, C. Zhang; Oscillation of solutions for second order nonlinear difference equations with nonlinear neutral term, Comput. Math. Appl. 41, 1487{1494, 2001.
Downloads
Published
License
Copyright (c) 2023 Kumar S. Vidhyaa, Ethiraju Thandapani, Jehad Alzabut, Abdullah Ozbekler
This work is licensed under a Creative Commons Attribution 4.0 International License.
