Semilinear Volterra Integrodifferential Equations with Nonlocal Initial Conditions

where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7] initiated the work concerning abstract nonlocal semilinear initial-value problems. He used fixedpoint methods to prove the existence and uniqueness of mild solutions to the Cauchy