Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators.
type: Item
instance of: scholarly article
title: Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators.
zbMATH Open document ID: 1050.47055
DOI: 10.1016/S0022-0396(02)00066-9
author: Athanassios G. Kartsatos
author: Zhengyuan Guan
author: Igor V. Skrypnik
published in: Journal of Differential Equations
publication date: 2003-04-02T00:00:00Z
review text: In a reflexive Banach space, the authors obtain a general ``ranges of sums'' result involving a maximal monotone operator \(A\) and a densely defined finitely continuous quasibounded generalized pseudomonotone operator \(B\). This result improves [\textit{F. E. Browder}, J. Funct. Anal. 25, 356--365 (1977; Zbl 0358.47037)], concerning everywhere defined continuous and bounded operators \(B\). Extensions of this theory are given using the degree theory of \textit{A. G. Kartsatos} and \textit{I. V. Skrypnik} [Trans. Am. Math. Soc. 354, 1601--1630 (2002; Zbl 1005.47058)] concerning densely defined perturbations of nonlinear maximal monotone operators with \((S_{+})\)-condition. Applications to nonlinear parabolic problems on cylindrical domains are given.
Mathematics Subject Classification ID: 47H14
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1891272
zbMATH Keywords: ranges of sums
zbMATH Keywords: maximal monotone operator
zbMATH Keywords: generalized pseudomonotone perturbation
zbMATH Keywords: generalized s-condition
zbMATH Keywords: degree theory
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891272