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
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
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.