A note on explicit criteria for the existence of positive solutions to the linear advanced equation ẋ(t)=c(t)x(t+τ)

The paper investigates a linear differential equation with advanced argument, ẋ(t)=c(t)x(t+τ), where τ>0, and the function c:[t0,∞)→(0,∞), t0∈R is bounded and locally Lipschitz continuous. New explicit criteria for the existence of a positive solution in terms of c and τ are derived. An overview of known relevant criteria is provided and relevant comparisons are also given.