具分段常数微分方程零解的全局吸引性

Global Attractivity for a Differential Equation with Piecewise Constant Arguments

考虑具分段常数微分方程x′(t)=r(t)f(x([t])),t 0,其中r(t)非负连续,f有下界且具有负Schwarz导数,f∈C3(R,R),xf(x)<0当x≠0,f′(0)<0,[.]表示最大整数函数,证明了当-f′(0)n∫+1nr(s)ds≤2且∞∫0r(s)ds=∞时,方程的零解是全局吸引的.

In this paper, we consider differential equation with piecewise constant arguments x＇（t）=r（t）f（x（[t]））,t≥0 where r f∈C^3（R,R）,xf（x）〈00 , if x ≠0 satisfying below bounded conditions and having everywhere negative Schwarz derivative. We obtained that if-f＇（0）∫n^n＋1r（s）ds≤2and∫0^∞ r（s）ds=∞, than the steady state solution x（t） = 0 ofthis equation is globally attracting.