On nonoscillatory solutions of two dimensional nonlinear delay dynamical systems

• Autorzy: Ozturk O. , Akin E.

Identyfikatory

DOI

10.7494/OpMath.2016.36.5.651

• Języki publikacji: EN

Abstrakty

EN

We study the classification schemes for nonoscillatory solutions of a class of nonlinear two dimensional systems of first order delay dynamic equations on time scales. Necessary and sufficient conditions are also given in order to show the existence and nonexis-tence of such solutions and some of our results are new for the discrete case. Examples will be given to illustrate some of our results.

Słowa kluczowe

EN

time scales; oscillation; two-dimensional dynamical system

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 5
• Strony: 651--669
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Ozturk O.

• Missouri University of Science and Technology 400 Rolla Building, Missouri 65409-0020, USA

autor

Akin E.

• Missouri University of Science and Technology 400 Rolla Building, Missouri 65409-0020, USA

Bibliografia

• [1] D.R. Anderson, Oscillation and nonoscillation criteria for two-dimensional time-scale systems of first order nonlinear dynamic equations, Electronic Journal of Differential Equations 2009 (2009) 24, 1-13.
• [2] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
• [3] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
• [4] P.G. Ciarlet, Linear and Nonlinear Functional Analysis with Applications, SIAM, Philadelphia, 2013.
• [5] T.S. Hassan, Oscillation criterion for two-dimensional dynamic systems on time scales, Tamkang Journal of Mathematics 44 (2013) 3, 227-232.
• [6] B. Knaster, Un theorems sur les fonctions d'ensembles, Ann. Soc. Polon. Math. 6 (1928), 133-134.
• [7] W. Li, Classification schemes for nonoscillatory solutions of two-dimensional nonlinear difference systems, Computer and Mathematics with Applications 42 (2001), 341-355.
• [8] W. Li, S. Cheng, Limiting behaviors of non-oscillatory solutions of a pair of coupled nonlinear differential equations, Proc. Edinb. Math. Soc. 43 (2000), 457-473.
• [9] Ó. Ózturk, E. Akm, Classification of nonoscillatory solutions of nonlinear dynamic equations on time scales, Dynamic Systems and Applications (2015), to appear.
• [10] Ó. Ózturk, E. Akm, Ż.U. Tiryaki, On nonoscillatory solutions of emden-fowler dynamic systems on time scales, Filomat (2015), to appear.
• [11] Ó. Ózturk, E. Akm, Nonoscillation criteria for two dimensional time scale systems (2015), submitted.
• [12] X. Zhang, Nonoscillation criteria for nonlinear delay dynamic systems on time scales, International Journal of Mathematical, Computational, Natural and Physcial Enginnering 8 (2014) 1.
• [13] S. Zhu, C. Sheng, Oscillation and nonoscillation criteria for nonlinear dynamic systems on time scales, Discrete Dynamics in Nature and Society (2012), Article ID 137471.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.