Asymptotic stability for scalar delay differential equations.

*(English)*Zbl 0930.34056The authors study the asymptotic stability of the zero solution to the scalar delay differential equation

$${x}^{\text{'}}\left(t\right)=F(t,x(\xb7))\phantom{\rule{2.em}{0ex}}(*)$$

which has been investigated by many authors. Here, they establish $\frac{3}{2}$-globally asymptotic stability conditions and the results obtained are new and interesting. As corollaries to their results, the main theorems by *J. R. Haddock* and *Y. Kuang* [J. Math. Anal. Appl. 168, No. 1, 147-162 (1992; Zbl 0764.45005)] are improved.

Reviewer: Wang Zhicheng (Changsha)

##### MSC:

34K20 | Stability theory of functional-differential equations |