Journal of Applied Mathematics and Stochastic Analysis
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.
Sergiu Aizicovici and Nikolaos S. Papageorgiou, “Extremal solutions to a class of multivalued integral equations in Banach space,” Journal of Applied Mathematics and Stochastic Analysis, vol. 5, no. 3, pp. 205-220, 1992. doi:10.1155/S1048953392000170