Stability of the zero solution of a family of functional-differential equations

摘要

We give some sufficient conditions under which the zero solution of the next functional-differential equationx′(t)=ax(t)+bx(τ0(t))+∑j=1kcjx′(τj(t))+f(x(t),x(τk+1(t)),…,x(τk+l(t))),where a,b,cj,j=1,k‾ are real numbers, f:Rl+1→R is a continuous function such that f(0,…,0)=0, and τj(t)∈C2[0,∞),j=0,k+l‾, is asymptotically stable.