Stability properties of solutions of linear Volterra integro-differential equations (Q760632)

Connections between the stability of \((1)\quad z'(t)=A(t)z(t)+\int^{t}_{0}C(t,s)z(s)ds\) and that of \((2)\quad z'(t)=A(t)z(t)+\int^{t}_{-\infty}C(t,s)z(s)ds\) are obtained. Here A and C are \(n\times n\) matrices of functions continuous for \(-\infty <t<\infty\) and \(-\infty <s\leq t<\infty\), respectively. Various necessary and sufficient conditions for the stability of the zero solution of (1) are given in terms of the solution of the resolvent equation.