New explicit integral criteria for the existence of positive solutions to the linear advanced equation

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