Abstract and Applied Analysis
Volume 7 (2002), Issue 6, Pages 295-322

On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications

Valeri Obukhovskii,1 Pietro Zecca,2 and Victor Zvyagin1

1Department of Mathematics, Voronezh University, Voronezh 394 006, Russia
2Dipartimento di Energetica “S. Stecco”, Università di Firenze, Firenze 50139, Italy

Received 10 December 2001

Copyright © 2002 Valeri Obukhovskii et al. 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.


We define a nonoriented coincidence index for a compact, fundamentally restrictible, and condensing multivalued perturbations of a map which is nonlinear Fredholm of nonnegative index on the set of coincidence points. As an application, we consider an optimal controllability problem for a system governed by a second-order integro-differential equation.