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

Ludwik Byszewski1 and Nikolaos S. Papageorgiou2

 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

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.