Making use of the generalized time scales exponential function, we give a new definition for the exponential stability of solutions for dynamic equations on time scales. Employing Lyapunov-type functions on time scales, we investigate the boundedness and the exponential stability of solutions to first-order dynamic equations on time scales, and some sufficient conditions are obtained. Some examples are given at the end of this paper.
Submitted January 16, 2006. Published January 8, 2007.
Math Subject Classifications:
Key Words: Time scale; Lyapunov-type function on time scales; boundedness; exponential stability.
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| Ai-Lian Liu |
Department of Statistics and Mathematics
Shandong Economics University
Jinan 250014, China
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