Nonuniform exponential dichotomy for block triangular systems on the half line
-
1940
Downloads
-
4338
Views
Authors
Le Huy Tien
- Department of Mathematics, Mechanics and Informatics, Vietnam National University at Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam.
Le Duc Nhien
- Department of Mathematics, Mechanics and Informatics, Vietnam National University at Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam.
Ta Van Chien
- Department of Mathematics, Mechanics and Informatics, Vietnam National University at Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam.
Abstract
In this paper, we discuss the nonuniform exponential dichotomy properties of nonautonomous systems of linear differential equations. Since any linear differential systems are kinematically similar to a triangular system, considering the relation between the nonuniform exponential dichotomy properties of the triangular system is necessary. Without loss of generality, we consider block upper triangular systems and give the criteria for the nonuniform exponential dichotomy of triangular systems on the half line for unbounded systems.
Share and Cite
ISRP Style
Le Huy Tien, Le Duc Nhien, Ta Van Chien, Nonuniform exponential dichotomy for block triangular systems on the half line, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 2, 85--96
AMA Style
Tien Le Huy, Nhien Le Duc, Chien Ta Van, Nonuniform exponential dichotomy for block triangular systems on the half line. J. Nonlinear Sci. Appl. (2020); 13(2):85--96
Chicago/Turabian Style
Tien, Le Huy, Nhien, Le Duc, Chien, Ta Van. "Nonuniform exponential dichotomy for block triangular systems on the half line." Journal of Nonlinear Sciences and Applications, 13, no. 2 (2020): 85--96
Keywords
- Nonuniform exponential dichotomy
- triangular system
- exponential dichotomy
MSC
References
-
[1]
L. Barreira, D. Dragičević, C. Valls, Fredholm Operators and Nonuniform Exponential Dichotomies, Chaos Solitons Fractals, 85 (2016), 120--127
-
[2]
L. Barreira, D. Dragičević, C. Valls, Nonuniform exponential dichotomies and Fredholm operators for flows, Aequationes Math., 91 (2017), 301--316
-
[3]
L. Barreira, D. Dragičević, C. Valls, Nonuniform exponential dichotomies and Lyapunov functions, Regul. Chaotic Dyn., 22 (2017), 197--209
-
[4]
L. Barreira, Y. Pesin, Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents, Encyclopedia of Mathematics and its Applications, Cambridge Univ. Press, Cambridge (2007)
-
[5]
L. Barreira, C. Valls, Stable manifolds for nonautonomous equations without exponential dichotomy, J. Differential Equations, 221 (2006), 58--90
-
[6]
L. Barreira, C. Valls, Stability of Nonautonomous Differential Equations, Springer, Berlin (2008)
-
[7]
L. Barreira, C. Valls, Nonuniform exponential dichotomies and admissibility, Discrete Contin. Dyn. Syst., 30 (2011), 39--53
-
[8]
L. Barreira, C. Valls, On two notions of exponential dichotomy, Dyn. Syst., 33 (2018), 708--721
-
[9]
F. Battelli, K. J. Palmer, Criteria for exponential dichotomy for triangular systems, J. Math. Anal. Appl., 428 (2015), 525--543
-
[10]
W. A. Coppel, Dichotomies in Stability Theory, Springer-Verlag, Berlin (1978)
-
[11]
O. Perron, Die Stabilitatsfrage bei Differentialgleichungen, (German) Math. Z., 32 (1930), 703--728
-
[12]
L. F. Zhou, K. N. Lu, W. N. Zhang, Equivalences between nonuniform exponential dichotomy and admissibility, J. Differential Equations, 262 (2017), 682--747