Boundedness and Uniqueness of Solutions to Dynamic Equations on Time Scales

In this work, we investigate the boundedness and uniqueness of solutions to systems of dynamic equations on time scales. We define suitable Lyapunov-type functions and then formulate appropriate inequalities on these functions that guarantee all solutions to first-order initial value problems are uniformly bounded and/or unique. Several examples are given. †cct@maths.unsw.edu.au