Asymptotic behavior of solutions of linear delay equations

The delay differential equations of the formx′(t)=?a(t)x(t?1),t≥0 are considered, wherea(t)≥0 is locally integrable on 0,∞). The main result: Let 0<c(t)≤a(t)≤k(t) for large ∫^∞, andc(t)≤Mc(t′) fort, t′≥T,|t?t′|≤l with some constantsl>0,M>1,T≥0. Then the condition \(k(t) \leqslant \frac{3}{2} + \alpha c(t), t \geqslant T\) with some constant α>0 dependent onl, M, ensures that all solutions of (*) tend to zero ast→∞.