New explicit integral criteria for the existence of positive solutions to the linear advanced equation ẏ(t)=c(t)y(t+τ)

The paper is devoted to the investigation of a linear differential equation with advanced argument y′(t)=c(t)y(t+τ)y′(t)=c(t)y(t+τ) where τ>0τ>0 is a constant advanced argument and the function c:[t0,∞)→[0,∞)c:[t0,∞)→[0,∞), t0∈Rt0∈R is bounded and locally Lipschitz continuous. New explicit integral criteria for the existence of a positive solution in terms of cc and ττ are derived and their efficiency is demonstrated.