Periodic and boundary value problems for second order differential inclusions

Palmucci, Michela; Papalini, Francesca

doi:https://doi.org/10.1155/S1048953301000120

International Journal of Stochastic Analysis

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Volume 14 |Article ID 840981 | https://doi.org/10.1155/S1048953301000120

Michela Palmucci, Francesca Papalini, "Periodic and boundary value problems for second order differential inclusions", International Journal of Stochastic Analysis, vol. 14, Article ID 840981, 22 pages, 2001. https://doi.org/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, Italy

²University of Ancona, Department of Mathematics, Via Brecce Bianche, Italy

Received01 Mar 1999

Revised01 Aug 1999

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.

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Copyright © 2001 Hindawi Publishing Corporation. 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.

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