Oscillation Result for Nonlinear Fourth-Order Homogeneous Neutral Delay Dynamic Equations
DOI:
https://doi.org/10.18311/jims/2022/29630Keywords:
Oscillation, Non-Linear, Neutral Delay Dynamic Equations, Time Scales.Abstract
We introduce an oscillatory result for fourth order homogeneous neutral delay dynamic equations on time scales, which deals with a unification and extension of the differential and difference equations depending upon the time scale defines on a continuous set and a discrete set respectively.Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 N. Sikender, S. Rakmaiah
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-01-30
Published 2022-08-23
References
Z. Bartosiewicz and E. Pawluszewicz, Realization of nonlinear control systems on time scales, IEEE Trans. Autom. Control, 53(2) (2008), 571–575. DOI: https://doi.org/10.1109/TAC.2007.914243
A. Bellen, N. Guglielmi and A. E. Ruehli, Methods for linear systems of circuit delay di?erential equations of neutral type, IEEE Trans. Circ. Systems-I, 46 (1999), 212–216. DOI: https://doi.org/10.1109/81.739268
M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkh¨auser, Boston, 2001. DOI: https://doi.org/10.1007/978-1-4612-0201-1
M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2003. DOI: https://doi.org/10.1007/978-0-8176-8230-9
S. Hilger, Analysis on measure chains: a uni?ed approach to continuous and discrete calculus, Results. Math., 18 (1990), 18–56. DOI: https://doi.org/10.1007/BF03323153
Y. Kuang, Delay Di?erential Equations with Applications in Population Dynamics, Academic Press, New Work, 1993.
A. B. Malinowska and D. F. M. Torres, Necessary and su?cient conditions for local pareto optimality on time scales, J. Math. Sci., 161(6) (2009), 803–810. DOI: https://doi.org/10.1007/s10958-009-9601-1
S. Panigrahi and P. Rami Reddy, On oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Comp. Math. Appl., 62 (2011), 4258–4271. DOI: https://doi.org/10.1016/j.camwa.2011.10.013
N. Sikender, P. Rami Reddy, M. Chenna Krishna Reddy and S. V. Sailaja, Classi?cation of solutions of non-homogeneous non-linear second order neutral delay dynamic equations with positive and negative coe?cients, Appl. Appl. Math., 4 (2019), 135–149.
N. Sikender, P. Rami Reddy and P. S. N. Reddy, Classi?cation of solutions of second order nonlinear non-homogeneous neutral mixed delay dynamic equations, AIP Conference Proceedings, 2246 (2020), 0200601–0200609. DOI: https://doi.org/10.1063/5.0014527
C. Soria-Hoyo, F. Pontiga and A. Castellanos, A PIC based procedure for the integration of multiple time scale problems in gas discharge physics, J. Comput. Phys., 228 (2009), 1017–1029. DOI: https://doi.org/10.1016/j.jcp.2008.10.007
A. K. Tripathy, New oscillation criteria for fourth order neutral dynamic equations, Commun. Appl. Anal., 20 (2016), 13–24.
F. Uysal and F. M. Atici, A production inventory model of HMMS on time scales, Appl. Math. Lett., 21 (2008), 236–243. DOI: https://doi.org/10.1016/j.aml.2007.03.013
W. Xiong and J. Liang, Novel stability criteria for neutral systems with multiple time delays, Chaos, Solitons and Fractals, 32 (2007), 1735–1741. DOI: https://doi.org/10.1016/j.chaos.2005.12.020
Chenghui Zhanga, Tongxing Li, Ravi P. Agarwal and Martin Bohner, Oscillation results for fourth-order nonlinear dynamic equations, Appl. Math. Lett., 25 (2012), 2058–2065. DOI: https://doi.org/10.1016/j.aml.2012.04.018