Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 2, Pages 161-182
doi:10.1155/S1048953301000120

Periodic and boundary value problems for second order differential inclusions

Michela Palmucci1 and Francesca Papalini2

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.

Abstract

In this paper we study differential inclusions with boundary conditions in which the vector field F(t,x,y) is a multifunction with Caratheodory type conditions. We consider, first, the case which F has values in ℝ 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 F takes their values in a Hilbert space.