Delay dynamic equations on time scales

Abstract

This article is concerned with delay dynamic equations on time scales. Linear and nonlinear delay dynamic equations are discussed. By using a different theorem to that used S. Hilger, Analysis on measure chains. A unified approach to continous and discrete calculus. Results Math. 18 (1990), pp. 18–56], some criteria for the existence, uniqueness and continuous dependence of the solution for the nonlinear delay dynamic equations are established.

Keywords:

• delay
• dynamic equation
• time scale
• existence
• uniqueness

AMS Subject Classifications::

• 34B15
• 34B20

Acknowledgements

This work was partially supported the NNSF of China (10961020), the China Postdoctoral Science Foundation (20070421106), the Key Project of Chinese Ministry of Education (208154) and the Science Foundation of Shanxi Province of China (2006011013).