Abstract
A distributed control problem for a hyperbolic system with mixed control-state constraints involving operator of infinite order is considered. The performance index is more general than the quadratic one and has an integral form. Making use of the Dubovitskii–Milyutin theorem,the optimality conditions for the Neumann problem are derived. Yet the problem considered here is more general than the problems in El-Zahaby [proceedings of the International conference on mathematics (Trends and Developments) of the Egyptian Mathematical Society, Cairo, Egypt, 28–31 December 2002, and Submitted for Publication in J Egyptian Math soc], Gali and El-Saify [proceedings of the International conference on functional–differential systems and related topics, vol III, Poland, 1983, pp 99–103] and Gali et al. [proceedings of the International conference on functional–differential systems and related topics, vol III, Poland, 1983, pp 83–87].