Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

1 Issue per year

Mathematical Citation Quotient (MCQ) 2016: 0.56

Emerging Science

Open Access
See all formats and pricing
More options …

Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Özkan Öztürk / Elvan Akın
Published Online: 2016-03-30 | DOI: https://doi.org/10.1515/msds-2016-0001


We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Keywords: Time-scale systems; Nonoscillation; Dynamic Equations


  • [1] D. R. Anderson, Oscillation and Nonoscillation Criteria for Two-dimensional Time-Scale Systems of First-Order Nonlinear Dynamic Equations. Electron. J. Differential Equations, Vol. 2009 (2009), No. 24, pp 1-13. Google Scholar

  • [2] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston, 2001. Google Scholar

  • [3] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, 2003. Google Scholar

  • [4] P. G. Ciarlet, Linear and Nonlinear Functional Analysis with Applications. Siam, 2013. Google Scholar

  • [5] T. S. Hassan, Oscillation Criterion for Two-Dimensional Dynamic Systems on Time Scales. Tamkang J. Math., Volume 44 (2013), Number 3, 227-232. Google Scholar

  • [6] B. Knaster, Un th´eor`eme sur les fonctions d’ensembles. Ann. Soc. Polon. Math. 6 (1928)133-134. Google Scholar

  • [7] Ö. Öztürk and E. Akın, Classification of Nonoscillatory Solutions of Nonlinear Dynamic Equations on Time Scales. Dynam. Systems. Appl. To appear, 2015. Google Scholar

  • [8] Ö. Öztürk, E. Akın and I. U. Tiryaki, On Nonoscillatory Solutions of Emden-Fowler Dynamic Systems on Time Scales. FILOMAT. To appear, 2015. Google Scholar

  • [9] W. Li, S. Cheng, Limiting Behaviors of Non-oscillatory Solutions of a Pair of Coupled Nonlinear Differential Equations. Proc. Edinb. Math. Soc. (2000) 43, 457-473. Google Scholar

  • [10] W. Li, Classification Schemes for Nonoscillatory Solutions of Two-Dimensional Nonlinear Difference Systems. Comput.Math. Appl. 42 (2001) 341-355. CrossrefGoogle Scholar

  • [11] X. Zhang, Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales. International Journal of Mathematical, Computational, Natural and Physcial Enginnering Vol:8 (2014), No:1. Google Scholar

  • [12] S. Zhu and C. Sheng, Oscillation and nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales. Discrete Dynamics in Nature and Society , Volume 2012, Article ID 137471. Google Scholar

About the article

Received: 2015-09-21

Accepted: 2016-02-03

Published Online: 2016-03-30

Citation Information: Nonautonomous Dynamical Systems, Volume 3, Issue 1, Pages 1–13, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2016-0001.

Export Citation

©2016 Özkan Öztürk and Elvan Akın. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Elvan Akın and Özkan Öztürk
Mediterranean Journal of Mathematics, 2017, Volume 14, Number 1

Comments (0)

Please log in or register to comment.
Log in