Stability for first order delay dynamic equations on time scales

AbstractIn this paper, we establish some sufficient conditions for the uniform stability and the uniformly asymptotical stability of the first order delay dynamic equation xΔ(t)+p(t)x(t−τ(t))=0,t∈T, where T is a time scale, p(.) is rd-continuous and positive, the delay function τ:T→(0,r]. Our results unify the corresponding ones for differential and difference equations. To the best of our knowledge, this is the first time to discuss the asymptotical behavior of delay dynamic equations on time scales