A fixed point index approach to Krasnosel'skiĭ-Precup fixed point theorem in cones and applications. (January 2023)

• Record Type: Journal Article
• Authors: Rodríguez–López, Jorge
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: 47H10 -- 47H11 -- 45G15 -- 34B18 -- 35J92; Coexistence fixed point -- fixed point index -- positive solution -- Hammerstein systems -- p-Laplacian system -- radial solution; 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.2022.113138
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We present an alternative approach to the vector version of Krasnosel'skiĭ compression–expansion fixed point theorem due to Precup, which is based on the fixed point index. It allows us to obtain new general versions of this fixed point theorem and also multiplicity results. We emphasize that all of them are coexistence fixed point theorems for operator systems, that means that every component of the fixed points obtained is non-trivial. Finally, these coexistence fixed point theorems are applied to obtain results concerning the existence of positive solutions for systems of Hammerstein integral equations and radially symmetric solutions of ( p 1, p 2 ) -Laplacian systems.