Compactness and existence results for ordinary differential equations in Banach spaces

DOI10.4171/ZAA/899zbMath0964.34048MaRDI QIDQ1806180

Alfonso Vignoli, Martin Väth, Jürgen Appell

Publication date: 20 December 1999

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

Full work available at URL: https://eudml.org/doc/48801

zbMATH Keywords

local weak solutionsPicard-Lindelöf operator

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Nonlinear differential equations in abstract spaces (34G20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Integral operators (45P05)

Related Items (3)

Compactness estimates for integral operators of vector functions with nonmeasurable kernels ⋮ On Darbo's fixed point principle ⋮ A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions

Cites Work

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• On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions
• Theorems of ascoli type involving measures of noncompactness
• On a fixed point principle of Sadovskii

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