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A linear system of delayed differential equations with multiple delays x ̇ (t) = − ∑ i = 1 s c i (t) A i (t) x (t − τ i (t)) , t ∈ [ t 0 , ∞) , is considered where x is an n -dimensional column vector, t 0 ∈ R , s is a fixed integer, delays τ i are positive and bounded, entries of n by n matrices A i as well as functions c i are nonnegative, and the sums of columns of the matrix A i (t) are identical and equal to a function α i (t). It is proved that, on [ t 0 , ∞) , the system has a solution with positive coordinates if and only if the scalar equation y ̇ (t) = − ∑ i = 1 s c i (t) α i (t) y (t − τ i (t)) , t ∈ [ t 0 , ∞) , has a positive solution. Some asymptotic properties of solutions related to both equations are also discussed. Illustrative examples are considered and some open problems formulated. • System of delayed differential equations. • Scalar delayed differential equations. • Multiple delays. • Novel positivity criterion. • Topological principle. [ABSTRACT FROM AUTHOR]

Abstract A new criterion for the existence of positive solutions of the second-order delayed differential equation y ̈ (t) = f (t , y t , y ̇ t) , t ∈ [ t 0 , ∞) is given with applications to linear equations. Open problems for future research are formulated. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with an impulsive neutral differential equation of Euler form with unbounded delays Sufficient conditions are obtained for every solution of (∗) to tend to a constant as . [Copyright &y& Elsevier]

Abstract: The asymptotic behavior of the bounded solutions of the delayed system is investigated, where is a given constant, , , is strictly increasing on , and either for all or for all . It is shown that every bounded solution of the system tends to a constant vector as . The result obtained extends the existing ones in the literature. [Copyright &y& Elsevier]