The essential spectral radius of Volterra operators and an application to Volterra-Hammerstein functional inclusions

DOI10.1007/s11117-008-2158-2zbMath1161.45009OpenAlexW2053252686WikidataQ57363392 ScholiaQ57363392MaRDI QIDQ1007087

Martin Väth

Publication date: 27 March 2009

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-008-2158-2

zbMATH Keywords

measure of noncompactnessessential spectrumLeray-Schauder alternativemultivalued mapsnonlinear integral equationabstract Volterra operatorVolterra-Hammerstein functional inclusion

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Integral operators (45P05) Eigenvalue problems for integral equations (45C05)

Cites Work

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• Measures of non-compactness of operators on Banach lattices
• Continuous selections. I
• On the spectral theory of elliptic differential operators. I
• Continuity, compactness, and degree theory for operators in systems involving \(p\)-Laplacians and inclusions
• Measures of non-compactness of operators in Banach lattices
• Abstract Volterra equations of the second kind
• An abstract Gronwall lemma and applications to global existence results for functional differential and integral equations of fractional order
• On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions
• Implicit function theorem in topological spaces
• Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
• Invariance of the essential spectrum
• The radius of the essential spectrum
• An axiomatic approach to a coincidence index for noncompact function pairs