Limiting Equations of Integrodifferential Equations in Banach Space

The "limiting equation" results for integrodifferential equations in finite dimensional space are extended to equations [formula] and [formula] in reflexive Banach space in a weak sense when A is a closed and densely defined operator and F(t) is a bounded operator t ≥ 0. The results are applied to study the periodic solutions of Eq. (b) on R. An application to a heat equation is also given.