This is an interesting paper in which the author extends the famous results by Yorke and Yoneyama to the functional-differential equation with instantaneous linear term
where is a constant, and is a piecewise continuous function.
However, many related references are missed, perhaps due to the large delay between submitting and publishing. Indeed, at least for constant and constant delay , the main results for are not new. For example, in this case, condition (2.6) in Theorem 2.3 reads
As it was noticed in [A. Ivanov, E. Liz and S. Trofimchuk, Tohoku Math. J., II. Ser. 54, No. 2, 277–295 (2002; Zbl 1025.34078)], under such a condition, the convergence of all solutions of (1) to zero was already proved by S. E. Grossman in a report from 1969. The sharp nature of the condition and its relations with the theorems were shown in the mentioned paper by Ivanov et al. Moreover, such a condition implies the global attractivity of the equilibrium under a condition much more general than the usual Yorke condition, as it was proved in [E. Liz, V. Tkachenko and S. Trofimchuk, SIAM J. Math. Anal. 35, No. 3, 596–622 (2003; Zbl 1069.34109)].
In any case, the results of the paper by Tang are a good contribution to the subject, since he considers the case of nonautonomous instanteneous term, and some results for . When , a more general result was recently proved in [T. Faria, E. Liz, J. J. Oliveira and S. Trofimchuk, Discrete Contin. Dyn. Syst. 12, 481–500 (2005; Zbl 1074.34069)].