Using Schaefer fixed point theorem, we establish a set of sufficient condition for the existence of mild solutions of nonlinear integrodifferential equations in Banach space.

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In this paper we prove the convexity and the compactness of the cores of targets for neutral control systems. We make use of a weak compactness argument; but in the crucial part where we establish the boundedness of the cores of the target we make use of the notion of asymptotic direction from Convex Set Theory. Let E n be n-dimensional Euclidean space. We prove that the core of the target H = L + E (where L = {x 6 E n | Mx = 0} , M is a constant m xn matrix and E is a compact, convex set containing 0) of the neutral systemis convex, and is compact if, and only if, the systemis Euclidean controllable.