Certain tests of stability for functional-differential equations, resolved with respect to derivative (Q1317577)

The equation \(x'(t)=\int^ t_ \tau x(s) d_ s r(t,s)\), \(t \geq \tau\) is considered; the ``Cauchy function'' is defined by \(x(t)=C (t,\tau) x(\tau)\), \(t \geq \tau\). Stability properties of the equations are discussed in terms of the Cauchy function, depending on various assumptions concerning the function \(r\) of bounded variation.