Nikolaos S Papageorgiou
Articles written in Proceedings – Mathematical Sciences
Volume 100 Issue 1 April 1990 pp 65-77
In this paper we examine infinite-dimensional control systems governed by semilinear evolution equations and having both state and control constraint. We introduce the relaxed system and show that the original trajectories are dense in an appropriate function space in the relaxed ones. We also determine the dependence of the solution set on the initial conditions. Then using those results we establish necessary and sufficient conditions for optimality for some optimization problems. Finally we prove some controllability results.
Volume 101 Issue 2 August 1991 pp 63-70
In this paper we prove some convergence theorems for Banach space valued multifunctions. First we consider the notion of weak convergence of sets and prove a weak completeness and a weak compactness result of the Dunford-Pettis type for weakly compact, convex valued integrable multifunctions. Then we consider set valued martingales and establish two convergence theorems. One using the Kuratowski-Mosco mode of convergence and for the other the Hausdorff mode.