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.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
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)
关键词
动力方程
时标
稳定性
渐近稳定性
dynamic equation
time scales
stability
asymptotic stability