Sous-potentiels d'un opérateur nonlinéaire. (Subpotentials of a nonlinear operator)
type: Item
instance of: scholarly article
title: Sous-potentiels d'un opérateur nonlinéaire. (Subpotentials of a nonlinear operator)
zbMATH Open document ID: 0639.47045
DOI: 10.1007/BF02776303
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let X be an ordered linear space and A be a nonlinear operator in X such that \((I+\lambda A)^{-1}\) is defined and non-decreasing for small \(\lambda >0\). Given \(v\in X\), any element \(u\in X\) satisfying \(u\leq (I+\lambda A)^{-1}(u+\lambda v)\) is called sub-potential of v. The authors study some properties of sub-potentials, as well as relations with subsolutions of the problem Au\(\ni v\). Moreover, they obtain a ``nonlinear analogue of the Kato inequality [see e.g. \textit{W. Arendt}, ``One-parameter semigroups of positive operators'', Lect. Notes Math. 1184 (1986; Zbl 0585.47030)].
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 4042644
zbMATH Keywords: nonlinear analogue of the Kato inequality
zbMATH Keywords: sub-potential
zbMATH Keywords: subsolutions
author: Louise Barthélémy
author: Philippe Benilan
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: One-parameter semigroups of positive operators
cites work: Problème d'obstacle pour une équation quasi-linéaire du premier ordre
cites work: Q5680673
cites work: Q4199298
cites work: Q3953613
cites work: Q5789040
cites work: Q5665783
cites work: Équations et inéquations non linéaires dans les espaces vectoriels en dualité
cites work: Q3032865
cites work: Q3220854
cites work: Q3785461
cites work: Q5512463
cites work: Q3946669
full work available at URL: https://doi.org/10.1007/bf02776303
OpenAlex ID: W2390396449
description: scientific article; zbMATH DE number 4042644