Abstract and Applied Analysis 
Volume 7 (2002), Issue 6, Pages 295-322
doi:10.1155/S1085337502002853

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

Abstract

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.