Abstract and Applied Analysis
Volume 1 (1996), Issue 4, Pages 381-396
doi:10.1155/S1085337596000206
On a local degree for a class of multi-valued vector fields in
infinite dimensional Banach spaces
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.
Abstract
This paper is devoted to the development of a local degree for multi-valued vector
fields of the form f−F. 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.