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We give new necessary and sufficient conditions under which the zero solution of Ž . Lienard-type systems is globally asymptotically stable. To this end, we examine í Ž . whether all trajectories intersect the vertical isocline or not and ii whether all trajectories tend to the origin or not. We also apply our results to a pseudolinear system. ᮊ

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The aim of this paper is to give sufficient conditions for global attractivity of the zero solution of the nonlinear delay differential equation x'(t) = -p(t)f(x(t -7)).An example which guarantees that our $ stability condition is the best possible is d S 0 given. 0 1999 Academic Press

Abstract. For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.