Abstract. In the present paper the differential equation $$ \dot y(t)=\alpha(t)[y(t)-y(t-\tau(t))] $$ with positive coefficient $\alpha$ and with positive bounded delay $\tau$ (which can have the property $\tau(+\infty)=0$) is considered. Explicit tests for convergence of all its solutions (for $t\to +\infty$) are proved.
AMSclassification. 34K15, 34K25
Keywords. Asymptotic convergence, point test, integral test.