时标上动力方程的稳定性(英文)

Stability of dynamic equations on time scales

借助于Gronwall’s不等式讨论时标上形如xΔ=Ax+p(t)+f(t,x)的动力方程,建立该类方程解的稳定性定理,研究该类方程解的渐近性,并给出比较定理.在此基础上获得了时标上的新的渐近稳定性判别准则。

By using the generalized Gronwall＇s inequality,conditions under which the solutions to a time invariant dynamic equation of the form xΔ=Ax＋p（t）＋f（t,x） are presented.A sufficient condition for stability of the dynamic equation is investigated on time scales.In particular,the asymptotic behavior of solutions to certain kinds of dynamic equations is discussed and a new comparison theorem is established.By constructing comparison theorem,new asymptotic stability criteria are obtained for all solutions of dynamic equations.