Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 179-190
doi: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 Ludwik Byszewski and Nikolaos S. Papageorgiou. 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.