De Pascale, E.; Marino, G. On the proof of abstract Cauchy-Kowalewska type theorems: Some improvements. (English) Zbl 0797.35003 Dyn. Syst. Appl. 3, No. 2, 259-266 (1994). 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 Keywords:Nash-Moser technique; existence interval; admissible nonlinearities; abstract Cauchy-Kowalewska type theorems PDFBibTeX XMLCite \textit{E. De Pascale} and \textit{G. Marino}, Dyn. Syst. Appl. 3, No. 2, 259--266 (1994; Zbl 0797.35003)