A note on the abstract Cauchy-Kowalewski theorem

DOI10.3792/pjaa.64.102zbMath0666.35003OpenAlexW2016813426MaRDI QIDQ1117091

Kiyoshi Asano

Publication date: 1988

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.64.102

zbMATH Keywords

contraction mapping principleexistenceuniquenessboundednessabstract Cauchy problemLipschitz conditionintegral formscale of Banach spacesabstract Cauchy- Kowalewski theoremabstract nonlinear integral equation

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Theoretical approximation in context of PDEs (35A35) Cauchy-Kovalevskaya theorems (35A10)

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Cites Work

• Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde
• A note on a theorem of Nirenberg
• An abstract form of the nonlinear Cauchy-Kowalewski theorem
• Long time existence for a slightly perturbed vortex sheet