Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 2, Pages 161-182
Periodic and boundary value problems for second order differential inclusions
1University of Perugia, Department of Mathematics, Via Vanvitelli 1, Perugia 060123, Italy
2University of Ancona, Department of Mathematics, Via Brecce Bianche, Ancona 60131, Italy
Received 1 March 1999; Revised 1 August 1999
Copyright © 2001 Michela Palmucci and Francesca Papalini. 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.
In this paper we study differential inclusions with boundary conditions in
which the vector field is a multifunction with Caratheodory type
conditions. We consider, first, the case which has values in and we
establish the existence of extremal solutions in the order interval determined by the lower and the upper solution. Then we prove the existence of
solutions for a Dirichlet problem in the case in which takes their values
in a Hilbert space.