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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Mathematical Citation Quotient (MCQ) 2015: 0.33


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Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Özkan Öztürk
  • Missouri University of Science and Technology, 314 Rolla Building, MO, 65409-0020
/ Elvan Akın
  • Missouri University of Science and Technology, 314 Rolla Building, MO, 65409-0020
Published Online: 2016-03-30 | DOI: https://doi.org/10.1515/msds-2016-0001

Abstract

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

References

  • [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.

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

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

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

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

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

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

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

  • [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.

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

  • [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.

  • [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.

About the article

Received: 2015-09-21

Accepted: 2016-02-03

Published Online: 2016-03-30



Citation Information: Nonautonomous Dynamical Systems, 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. (CC BY-NC-ND 3.0)

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