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.