Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

• Autorzy: Özkan Öztürk , Elvan Akın
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Time-scale systems; Nonoscillation; Dynamic Equations

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 1-13

Daty

otrzymano

2015-09-21

zaakceptowano

2016-02-03

online

2016-03-30

Twórcy

autor

Özkan Öztürk

• Missouri University of Science and Technology, 314 Rolla Building, MO, 65409-0020

autor

Elvan Akın

• Missouri University of Science and Technology, 314 Rolla Building, MO, 65409-0020

Bibliografia

• [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.

Identyfikatory

DOI

10.1515/msds-2016-0001