QUALITATIVE ANALYSIS OF DYNAMIC EQUATIONS ON TIME SCALES USING LYAPUNOV FUNCTIONS

We employ Lyapunov functions to study boundedness and stability of dynamic equations on time scales. Most of our Lyapunov functions involve the term |x| and its ?-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 examples.