Linearized stability for nonlinear Volterra equations

In the context of the nonlinear Volterra equation u(t) + integral(t)(0) b(t - s) Au(s) ds is an element of u(0), t >= 0, with A. XxX anm-a-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution u(e) under the assumption of the existence of a resolvent-differential (A) over tilde subset of X x X of A at u(e) with the property that ((A) over tilde - omega I) is accretive for some omega > 0.