Abstract and Applied Analysis
Volume 1 (1996), Issue 4, Pages 381-396

On a local degree for a class of multi-valued vector fields in infinite dimensional Banach spaces

N. M. Benkafadar1 and B. D. Gel'man2

1Institut de Mathématiques, Université de Constantine, Route de Ain El-Bey, Constantine 25000, Algeria
2Mathematics Faculty, Voronezh State University, Universitetskaya Pl.1, Voronezh 394693, Russia

Received 17 June 1996

Copyright © 1996 N. M. Benkafadar and B. D. Gel'man. 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.


This paper is devoted to the development of a local degree for multi-valued vector fields of the form fF. Here, f is a single-valued, proper, nonlinear, Fredholm, C1-mapping of index zero and F is a multi-valued upper semicontinuous, admissible, compact mapping with compact images. The mappings f and F are acting from a subset of a Banach space E into another Banach space E1. This local degree is used to investigate the existence of solutions of a certain class of operator inclusions.