Topological Degree via a Degree of Nondensifiability and Applications

Abstract

The goal of this work is to introduce the notion of topological degree via the principle of the degree of nondensifiability (DND for short). We establish some new fixed point theorems, concerning, Schaefer’s fixed point theorem and the nonlinear alternative of Leray–Schauder type. As applications, we study the existence of mild solution of functional semilinear integro-differential equations.

Keywords

• degree of nondensifiability
• <i>α</i>-dense curves
• DND
• topological degree
• <i>k</i>−<i>φ_d</i>−contraction
• resolvent operator