Existence criteria for operator inclusions in abstract spaces
type: Item
instance of: scholarly article
title: Existence criteria for operator inclusions in abstract spaces
zbMATH Open document ID: 0956.47032
DOI: 10.1016/S0377-0427(99)00252-6
author: Ravi P. Agarwal
author: Donal O'Regan
published in: Journal of Computational and Applied Mathematics
publication date: 2000-02-03T00:00:00Z
review text: The authors obtain existence criteria for the operator equation \(y(t)= Fy(t)\) on \([0,T]\), in a Banach space. The results rely on fixed point theorem of Leray-Schauder type due to Mönch. In addition, the paper presents existence principles for operator inclusions of the form \(y(t)\in Fy(t)\) in Banach spaces. The tool in this case is the nonlinear alternative of Leray-Schauder type for condensing set-valued mappings. Applications are given to Hammerstein integral equations and inclusions.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1398403
zbMATH Keywords: operator equation
zbMATH Keywords: fixed point theorem of Leray-Schauder type
zbMATH Keywords: operator inclusions
zbMATH Keywords: condensing set-valued mappings
zbMATH Keywords: Hammerstein integral equations
reviewed by: Radu Precup
MaRDI profile type: Publication
cites work: Upper semicontinuity of Nemytskij operators
cites work: Q5185568
cites work: Q4860445
cites work: Volterra and Urysohn integral equations in Banach spaces
cites work: Q4212839
cites work: Q3983442
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description: scientific article; zbMATH DE number 1398403