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

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, $C^1$-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 $E_1$. This local degree is used to investigate the existence of solutions of a certain class of operator inclusions.