Algebraic multiplicity and topological degree for Fredholm operators. (December 2020)

• Record Type: Journal Article
• Authors: López-Gómez, Julián; Sampedro, Juan Carlos
• Is Part Of: Nonlinear analysis. Volume 201(2020)
• Publication Date: 2020-12
• Subjects: 47H11 -- 58C40; Schauder formula -- Fredholm paths -- Leray–Schauder degree -- Degree of Fitzpatrick -- Pejsachowicz and Rabier -- Generalized algebraic multiplicity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.112019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper tries to establish a link between topological and algebraic methods in nonlinear analysis showing how the topological degree for Fredholm operators of index zero of Fitzpatrick et al. (1994) can be determined from the generalized algebraic multiplicity of Esquinas and López-Gómez (1988, 2001), in the same vein as the Leray–Schauder degree can be calculated from the Schauder formula through the classical algebraic multiplicity.