On the exponential stability of dynamic equations on time scales (Q878484)

The authors prove various results on exponential stability of linear and nonlinear dynamic equations \( x^\Delta (t) = F(t,x) \) on a time scale \(\mathbb{T}\) ( = arbitrary closed subset of the reals). There are theorems on linearized stability, Perron's Theorem about input-output stability, a characterization of uniform exponential stability of linear equations. Since the paper deals with bounded below time scales the usual condition of regressivity of the equation can be dropped.