On Nonoscillation of Systems of Delay Equations

Abstract

The paper investigates nonnegativity of all entries of the fundamental matrix for the system of linear delay differential equations $\dot{X}$(t)+$\sum_{k=1}^m$ A_k(t)X(h_k(t))=0 in the case when the non-diagonal entries of matrices A_k are nonpositive. The results are applied to study nonoscillation of high order differential equations, as well as exponential stability for systems of delay equations.