Stability theorem for a class of nonautonomous neutral differential equations with unbounded delay

Consider the one-dimensional nonautonomous neutral differential equation d/dt[x(t)-f(t,x(p(t)))] + f(t,x(q(T))) = o, t greater than or equal to t(0), where p, q : [t(0), infinity) --> R are continuous and strictly increasing, p(t) < t, q(r) < t for all t greater than or equal to t(0), and xg(t,x) greater than or equal to 0 for t greater than or equal to t(o), x is an element of R, in this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. (C) 2001 Academic Press.