Qualitative analysis of dynamic equations on time scales using Lyapunov functions

Abstract

. We employ Lyapunov functions to study boundedness and stability of dynamic equa- tions on time scales. Most of our Lyapunov functions involve the term | x | and its Δ -derivative. In particular, we prove general theorems regarding qualitative analysis of solutions of delay dynamical systems and then use Lyapunov functionals that partially include | x | to provide ex-amples.