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

Abstract

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+l̄, is asymptotically stable.