时标上动力方程的稳定性(英文)  

Stability of dynamic equations on time scales

作　　者：贾文奇[1] 杨军[1,2] 石胜利[1] 田宝亮[1] 

机构地区：[1]燕山大学理学院,秦皇岛066004 [2]河北省数学研究中心,石家庄050000

出　　处：《黑龙江大学自然科学学报》2010年第5期676-680,共5页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(60604004);the Natural Science Foundation of Hebei province(07M005)

摘　　要：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.

关 键 词：动力方程 时标 稳定性 渐近稳定性 

分 类 号：O193[理学—数学]