Topological degree theories and nonlinear operator equations in Banach spaces
type: Item
instance of: scholarly article
title: Topological degree theories and nonlinear operator equations in Banach spaces
zbMATH Open document ID: 1142.47346
author: Dhruba R. Adhikari
author: Athanassios G. Kartsatos
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-09-10T00:00:00Z
review text: Let \(X\) be a real Banach space, \(G_1\), \(G_2\) open and bounded such that \(0\in G_2\subset\bar{G}_2\subset G_1\). Let \(T:D(T)\to X\) be accretive such that \(0\in D(T)\) and \(T(0)=0\). Let \(C:D(C)\to X\) be compact or continuous and bounded with the resolvents of \(T\) compact. The authors use various degree theories to find zeros of \(T+C\) in \(D(T+C)\cap(G_1\setminus G_2)\). As a matter of fact, the article contains much more results: the range space may be \(X^*\) instead of \(X\) and \(C\) may belong to more complicated classes of operators. There is a short application to partial differential equations.
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47B44
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 5323989
zbMATH Keywords: maximal monotone operators
zbMATH Keywords: \(m\)-accretive operators
zbMATH Keywords: compact perturbations
zbMATH Keywords: compact resolvents
zbMATH Keywords: excision property
zbMATH Keywords: Leray-Schauder degree theory
zbMATH Keywords: Kartsatos-Skrypnik degree theory
zbMATH Keywords: nonzero solutions
reviewed by: Christian Fenske
MaRDI profile type: Publication
full work available at URL: j.na.2007.06.026
OpenAlex ID: W2083036978
cites work: Perturbations of nonlinear maximal monotone sets in banach space
cites work: Q4092518
cites work: Fixed point theory and nonlinear problems
cites work: Q3141921
cites work: Fixed point theorems for mappings in ordered Banach spaces
cites work: Q3999276
cites work: Nonzero solutions of nonlinear equations involving compact perturbations of accretive operators in Banach spaces
cites work: Q3994493
cites work: Noncompact mappings and cones in Banach spaces
cites work: Q4877749
cites work: Topological degree theories for densely defined mappings involving operators of type \((S_+)\)
cites work: Normalized eigenvectors for nonlinear abstract and elliptic operators
cites work: The index of a critical point for nonlinear elliptic operators with strong coefficient growth
cites work: The index of a critical point for densely defined operators of type \((S_+)_L\) in Banach spaces
cites work: Degree theories and invariance of domain for perturbed maximal monotone operators in Banach spaces
cites work: On the eigenvalue problem for perturbed nonlinear maximal monotone operators in reflexive Banach spaces
cites work: The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces
cites work: Q4281353
cites work: Q5732050
cites work: Q3904867
cites work: Degree of Mapping in Convex Linear Topological Spaces
cites work: Q4173851
cites work: Q3730503
cites work: Minimax monotonicity
cites work: Q4049449
cites work: Q4312115
cites work: Q3995594
DOI: 10.1016/J.NA.2007.06.026
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description: scientific article; zbMATH DE number 5323989