Journal of Applied Mathematics and Stochastic Analysis 
Volume 5 (1992), Issue 3, Pages 205-220
doi:10.1155/S1048953392000170

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

Abstract

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.