A note on explicit criteria for the existence of positive solutions to the linear advanced equation

The paper investigates a linear differential equation with advanced argument, x ̇ ( t ) = c ( t ) x ( t + τ ) , where τ > 0 , and the function c : [ t 0 , ∞ ) → ( 0 , ∞ ) , t 0 ∈ 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.