不动点和一类中立型方程的渐近稳定性(英文)  

Fixed Point and Asymptotic Stability of a Neutral Differential Equation

作　　者：丁黎明[1,2] 李志祥[1] 原野[3] 

机构地区：[1]国防科技大学理学院数学与系统科学系,湖南长沙410073 [2]空军雷达学院,湖北武汉430010 [3]空军工程大学理学院,陕西西安710051

出　　处：《应用数学》2009年第3期596-602,共7页Mathematica Applicata

摘　　要：本文用不动点定理研究了一类中立型泛函微分方程[x(t)-P(t)x(t-τ)]′+Q(t)x(t-r(t))=0,t≥t0的零解的渐近稳定性,其中τ∈(0,∞),P,Q∈C([t0,∞),R),r∈C([t0,∞),R+),且当t→∞时t-r(t)→∞.我们讨论了r(t)为常数和不为常数两种情况.所得定理改进和包含了前人已有的结果.The asymptotic stability of the zero solution of the scalar neutral functional differential equation [x(t)-P(t)x(t-τ)]'+Q(t)x(t-r(t))=0,t≥t0,is investigated by means of fixed point theory,where τ∈(0,∞),P,Q∈C([t0,∞),R)and r∈ C([t0,∞),R+)with t-r(t)→∞ as t→∞.The cases that r(t)is not constant and r(t)is constant are discussed respectively.The obtained theorems improve and generalize previous results.

关 键 词：不动点 渐近稳定 中立型泛函微分方程 

分 类 号：O175.1[理学—数学]