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On the proof of abstract Cauchy-Kowalewska type theorems: Some improvements. (English) Zbl 0797.35003

Summary: Enlargements in the existence interval and in admissible nonlinearities are obtained in abstract Cauchy-Kowalewska type theorems. The proof uses stronger than usual norm estimates and is based on the minimization of suitable natural functionals.

MSC:

35A10 Cauchy-Kovalevskaya theorems
34G20 Nonlinear differential equations in abstract spaces
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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