Solutions to non-autonomous integrodifferential equations with infinite delay

The conclusions of Da Prato and Sinestrari concerning the non-autonomous evolution operator of hyperbolic type for the equation u (t) = A(t)u(t) +f (t), t ∈ [0,T ], u(0) = z are applied to find the uniqueness and existence of solution to u (t) = A(t)u(t) + t 0 K t, θ,u(θ) dθ + L(t)ut +f (t), t ∈ [0,T ], u0 = ϕ, where A(·) maybe nondensely defined. Moreover, some relative problems are concerned. © 2006 Elsevier Inc. All rights reserved