On the optimal control of systems governed by nonlinear volterra equations

Existence theorems are stated and proved for optimal control problems monitored by a nonlinear Volterra-type integral equation. Growth conditions are taken into consideration which ensure the needed compactness on the set of trajectories and entail the existence of the usual optimal solutions for the given problem. Weak or approximate solutions are taken into consideration in a subsequent paper.The author would like to express his appreciation to Professor L. Cesari and Professor M. B. Suryanarayana for many helpful conversations and suggestions for the improvement of earlier versions of this paper.