There is a close connection between stability and oscillation of delay differential equations. For the first-order equation x′(t)+c(t)x(τ(t))=0,t≥0,
Nearby in the stack
where
c
is locally integrable of any sign,
τ(t)≤t
is Lebesgue measurable,
limt→∞τ(t)=∞
, we obtain sharp results, relating the speed of oscillation and stability. We thus unify the classical results of Myshkis and Lillo. We also generalise the
3/2−
stability criterion to the case of measurable parameters, improving