Asymptotic behavior of solutions of Volterra integro-differential equations

Abstract

The asymptotic behavior of solutions of Volterra integrodifferential equations of the form \[ x’(t) = A(t)x(t) + \int _0^t {K(t,s)} x(s)ds + F(t)\] is discussed in which $A$ is not necessarily a stable matrix. An equivalent equation which involves an arbitrary function is derived and a proper choice of this function would pave a way for the new coefficient matrix $B$ (corresponding $A$) to be stable.