ABSTRACT
In this chapter, we study stability of second order delay differential equations with variable coefficients and delays. The main idea is to construct the Cauchy functions for the second order linear ordinary differential equations and then to use W-transform. As a result, assertions in the form of inequalities on the smallness of delays and variation of the coefficients are obtained. The main development is achieved in exact estimates of integrals with respect to s of the Cauchy functions and their derivatives in t. This allows us to obtain best possible inequalities on the smallness of delays and variation of the coefficients. We demonstrate examples to compare our estimates with known ones.
