The conjecture on decay of oscillatory solutions below Lillo's constant

Consider the delay differential equation (1), with coefficient $c(t)$ and delay function $\Greekmath 011C (t)$ satisfying the assumptions in (10a). Assume that $c(t)\leq 0$ for $t\geq 0$ and

$$\sup_{t\geq \Greekmath 011A }\int_{\Greekmath 011C (t)}^t |c(\Greekmath 0110 )|\,d\Greekmath 0110 <2.75+\ln 2,$$

where $\Greekmath 011A$ satisfies (10a). Decay conjecture. All oscillatory solutions of (1) tend to zero. This would extend the known decay results up to the critical constant $2.75+\ln 2$; the source states that the problem remains open.