Boundedness and exponential stability of solutions to dynamic equations on time scales

Abstract

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.

Keywords

• Lyapunov-type function on time scales
• boundedness
• exponential stability.