Continuous dependence for integrodifferential equations with infinite delay (Q1185391)

The authors show, under certain conditions, that the solution of the integro-differential equation \(x'(t)=h(t,x(t))+\int_{-\infty}^ t q(t,s,x(s))ds+F(t,x(t),Sx(t))\), \(0\leq t\leq T\), \(x(t)=\varphi(t)\), \(- \infty<t\leq 0\), where \(Sx(t)=\int_{-\infty}^ t K(t,s,x(s))ds\), depends continuously, in some sense, on the initial function \(\varphi(t)\). The existence of a unique solution of the problem is one of their assumptions.