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 equationu′(t)=A(t)u(t)+f(t),t∈[0,T],u(0)=z are applied to find the uniqueness and existence of solution tou′(t)=A(t)u(t)+∫0tK(t,θ,u(θ))dθ+L(t)ut+f(t),t∈[0,T],u0=φ, where A(⋅)A(⋅) maybe nondensely defined. Moreover, some relative problems are concerned.