Nonuniform exponential dichotomy for block triangular systems on the half line

Volume 13, Issue 2, pp 85--96 http://dx.doi.org/10.22436/jnsa.013.02.02
Publication Date: September 26, 2019 Submission Date: May 30, 2019 Revision Date: August 06, 2019 Accteptance Date: August 26, 2019

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.


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