Leggett–Williams type theorems with applications to nonlinear differential and integral equations. (February 2015)

• Record Type: Journal Article
• Authors: Bugajewski, Dariusz; Kasprzak, Piotr
• Is Part Of: Nonlinear analysis. Volume 114(2015)
• Page Start: 116
• Page End: 132
• Publication Date: 2015-02
• Subjects: 47H10 -- 47H30 -- 45H30 -- 45M20 -- 34B18 -- 45G15 -- 45N05; Absolute retract -- Coupled fixed point -- Fixed point theorem -- Hammerstein integral equation -- Invariant direction -- Measure of noncompactness -- Ordered Banach space -- Rδ-set -- Reflection operator -- System of Hammerstein equations -- Two-point boundary value problem; 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.2014.11.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The aim of this article is to prove a few Leggett–Williams type theorems, in particular for a more general class of mappings than compact ones. We examine also invariant directions which satisfy a certain additional condition formulated in terms of a given seminorm. As applications of these results we prove a few existence results concerning positive solutions to Hammerstein integral equations or to a two-point boundary value problem.