Stability Criteria with a Symmetric Operator Occurring in Linear and Nonlinear Delay-Differential Equations

In a recent paper ([6]) this author has given theorems for delay - differential equations which are parallel to theorems of Markus and Yamabe on ordinary differential equations in their paper Global Stability Criteria for Differential Systems ([8]). In this paper we review the ideas for these theorems and we give new theorems putting these ideas in a broader, more flexible, and handier framework.