Table of Contents
Journal of Applied Mathematics and Stochastic Analysis
Volume 12, Issue 2, Pages 179-190
http://dx.doi.org/10.1155/S1048953399000180

An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem

1Cracow University of Technology, Institute of Mathematics, Warszawska 24, Cracow 31-155, Poland
2National Technical University, Department of Mathematics, Zografou Campus, Athens 15773, Greece

Received 1 January 1998; Revised 1 June 1998

Copyright © 1999 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.

Abstract

The aim of the paper is to prove two theorems on the existence of solutions to a nonlocal multivalued Darboux problem. The first theorem concerns the case when the orientor field is convex valued. The second theorem concerns the case when the orientor field is nonconvex valued. A compactness type condition involving the ball measure of noncompactness is applied.