Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 3, Pages 205-220

Extremal solutions to a class of multivalued integral equations in Banach space

Sergiu Aizicovici1 and Nikolaos S. Papageorgiou2

1Ohio University, Department of Mathematics, Athens 45701, OH, USA
2Florida Institute of Technology, Department of Applied Mathematics, Melbourne 32901, FL, USA

Received 1 March 1992; Revised 1 June 1992

Copyright © 1992 Sergiu Aizicovici and Nikolaos S. Papageorgiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a “bang-bang” theorem for a class of nonlinear, infinite dimensional control systems.