Abstract version of the Cauchy-Kowalewski problem

• Autorzy: Oleg Zubelevich
• Języki publikacji: EN

Abstrakty

EN

We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.

Słowa kluczowe

EN

weighted Banach space; Nishida's theorem; scales of Banach spaces; fixed point theorems; 35A10

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 3
• Strony: 382-387

Daty

wydano

2004-06-01

online

2004-06-01

Twórcy

autor

Oleg Zubelevich

• Moscow State Aviation Institute

Bibliografia

• [1] F. E. Browder: “A new generalization of the Schauder fixed point theorem”,Math. Ann.,Vol.174, (1967), pp.285–290. http://dx.doi.org/10.1007/BF01364275
• [2] L. Nirenberg: “An abstract form of the nonlinear Cauchy-Kowalewski theorem”,J. Differential Geometry, Vol. 6 (1972), pp. 561–576.
• [3] T. Nishida: “A Note On A Theorem Of Nirenberg”,J. Differential Geometry, Vol. 12, (1977), pp. 629–633.
• [4] L. Ovsjannikov: “Singular operators in Banach scales”,Dokl. Akad. Nauk. SSSR, Vol. 163, (1965), pp. 819–822. (Soviet Math. Dokl, Vol. 6, (1965), pp. 1025–1028).
• [5] M. Safonov: “The abstract Cauchy-Kovalevskaya theorem in a weighted Banach space”,J. Commun. Pure Appl. Math., Vol. 48, (1995), pp. 629–637.
• [6] L. Schwatz:Analyse Mathématique, Hermann, Paris, 1967.
• [7] J. Treves Ovsjannikov: “Theorem and hyperdiferential operators”,Notas Mat., Vol. 46, (1968), mimeographed notes.
• [8] T. Yamanaka: “Note on Kowalevskaja's system of partial differential equations”,Comment. Math. Univ. St. Paul, Vol. 9, (1960), pp. 7–10.

Identyfikatory

DOI

10.2478/BF02475235