On the stability region of scalar delay-differential equations (Q1114071)

The paper deals with the uniform stability of the zero solution to the functional differential equation \(\dot x(t)=F(t,x_ t)+G(t,x(t)),\) where \(| G(t,x)| \leq a(t)| x|\) and -b(t)[f]\(\leq F(t,f)\leq b(t)[-f]\), \([f]=\sup \{f(t): -q\leq t\leq 0\}\). The stability conditions are given in terms of the ``comparison'' equation \(\dot x(t)=a(t)x(t)- b(t)x(t-r(t)),\) \(0\leq r(t)\leq q\).