Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 3
152
Views
6
CrossRef citations to date
0
Altmetric
Research Article

On nonlinear impulsive differential systems with canonical and non-canonical operators

, &
Pages 852-864 | Received 06 Jul 2021, Accepted 29 Jul 2021, Published online: 20 Sep 2021

References

  • Bonotto EM, Gimenes LP, Federson M. Oscillation for a second-order neutral differential equation with impulses. Appl Math Comput. 2009;215(1):1–15.
  • Bainov DD, Simeonov PS. Impulsive differential equations: asymptotic properties of the solutions. Singapore: World Scientific; 1995. (Series on Advances in Mathematics for Applied Sciences; 28).
  • Lakshmikantham V, Bainov DD, Simeonov PS. Oscillation theory of impulsive differential equations. Singapore: World Scientific; 1989.
  • Agarwal RP, O'Regan D, Saker SH. Oscillation and stability of delay models in biology. New York (NY): Springer International Publishing; 2014.
  • Berezansky L, Domoshnitsky A, Koplatadze R. Oscillation, nonoscillation, stability and asymptotic properties for second and higher order functional differential equations. Boca Raton (FL): Chapman & Hall/CRC Press; 2020.
  • Shen JH, Wang ZC. Oscillation and asymptotic behaviour of solutions of delay differential equations with impulses. Ann Differ Eqs. 1994;10(1):61–68.
  • Graef JR, Shen JH, Stavroulakis IP. Oscillation of impulsive neutral delay differential equations. J Math Anal Appl. 2002;268:310–333.
  • Shen J, Zou Z. Oscillation criteria for first order impulsive differential equations with positive and negative coefficients. J Comput Appl Math. 2008;217:28–37.
  • Karpuz B, Ocalan O. Oscillation criteria for a class of first-order forced differential equations under impulse effects. Adv Dyn Syst Appl. 2012;7(2):205–218.
  • Tripathy AK, Santra SS. Characterization of a class of second order neutral impulsive systems via pulsatile constant. Differ Equ Appl. 2017;9(1):87–98.
  • Tripathy AK, Santra SS. Necessary and sufficient conditions for oscillation of a class of second order impulsive systems. Differ Equ Dyn Syst. 2018. https://doi.org/10.1007/s12591-018-0425-7.
  • Santra SS, Tripathy AK. On oscillatory first order nonlinear neutral differential equations with nonlinear impulses. J Appl Math Comput. 2019;59:257–270. https://doi.org/10.1007/s12190-018-1178-8.
  • Santra SS, Dix JG. Necessary and sufficient conditions for the oscillation of solutions to a second-order neutral differential equation with impulses. Nonlinear Stud. 2020;27(2):375–387.
  • Tripathy AK, Santra SS. On the forced impulsive oscillatory nonlinear neutral systems of the second order. Nonlinear Oscil. 2020;23(2):274–288.
  • Tripathy AK, Santra SS. Necessary and sufficient conditions for oscillations to a second-order neutral differential equations with impulses. Kragujev J Math. 2023;47(1):81–93.
  • Bazighifan O, Ruggieri M, Scapellato A. An improved criterion for the oscillation of fourth-order differential equations. Mathematics. 2020;8(4):610. https://doi.org/10.3390/math8040610.
  • Bazighifan O, Ruggieri M, Santra SS, et al. Qualitative properties of solutions of second-order neutral differential equations. Symmetry. 2020;12(9):1520. https://doi.org/10.3390/sym12091520.
  • Berezansky L, Braverman E. Oscillation of a linear delay impulsive differential equations. Commun Appl Nonlinear Anal. 1996;3:61–77.
  • Diblik J, Svoboda Z, Smarda Z. Retract principle for neutral functional differential equation. Nonlinear Anal Theory Methods Appl. 2009;71(12):1393–1400.
  • Diblik J. Positive solutions of nonlinear delayed differential equations with impulses. Appl Math Lett. 2017;72:16–22.
  • Luo Z, Jing Z. Periodic boundary value problem for first-order impulsive functional differential equations. Comput Math Appl. 2008;55:2094–2107.
  • Yu J, Yan J. Positive solutions and asymptotic behavior of delay differential equations with nonlinear impulses. J Math Anal Appl. 1997;207:388–396.
  • Tripathy AK. Oscillation criteria for a class of first order neutral impulsive differential-difference equations. J Appl Anal Comput. 2014;4:89–101.
  • Santra SS, Majumder D, Bhattacharjee R, et al. New theorems for oscillations to the differential equations with mixed delays. Symmetry. 2021;13(3):367.
  • Agarwal RP, Bazighifan O, Ragusa MA. Nonlinear neutral delay differential equations of fourth-order: oscillation of solutions. Entropy. 2021;23:129.
  • Bazighifan O, Ragusa MA. Nonlinear equations of fourth order with p-Laplacian like operator: oscillation, methods and applications. Proc Am Math Soc. 2021. https://doi.org/10.1090/proc/15794.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.