Continuity and differentiability of multivalued superposition operators with atoms and parameters. I.

DOI10.4171/ZAA/1450zbMath1237.47065OpenAlexW2031254218WikidataQ57363355 ScholiaQ57363355MaRDI QIDQ656126

Martin Väth

Publication date: 26 January 2012

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1450

zbMATH Keywords

continuityatomOrlicz spaceNemytskij operatorLebesgue-Bochner spacemultivalued mapsuperposition operatorparameter dependenceuniform differentiabilityBochner ideal spacesgeneralized ideal space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Set-valued operators (47H04)

Related Items (3)

Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas ⋮ Evolution problems with nonlinear nonlocal boundary conditions ⋮ On strongly condensing operators

Cites Work

• Bifurcation for a reaction-diffusion system with unilateral obstacles with pointwise and integral conditions
• Bifurcation points for a reaction-diffusion system with two inequalities
• Global bifurcation for a reaction-diffusion system with inclusions
• Multivalued superposition operators in ideal spaces of vector functions. II
• Ideal spaces
• Smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem.
• Degree and global bifurcation for elliptic equations with multivalued unilateral conditions
• Über die Differenzierbarkeit des Superpositions-Operators in Orlicz-Räumen
• Upper estimates for superposition operators and some applications
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