# Abstract version of the Cauchy-Kowalewski problem

Open Mathematics (2004)

- Volume: 2, Issue: 3, page 382-387
- ISSN: 2391-5455

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topOleg Zubelevich. "Abstract version of the Cauchy-Kowalewski problem." Open Mathematics 2.3 (2004): 382-387. <http://eudml.org/doc/268741>.

@article{OlegZubelevich2004,

abstract = {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.},

author = {Oleg Zubelevich},

journal = {Open Mathematics},

keywords = {35A10},

language = {eng},

number = {3},

pages = {382-387},

title = {Abstract version of the Cauchy-Kowalewski problem},

url = {http://eudml.org/doc/268741},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Oleg Zubelevich

TI - Abstract version of the Cauchy-Kowalewski problem

JO - Open Mathematics

PY - 2004

VL - 2

IS - 3

SP - 382

EP - 387

AB - 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.

LA - eng

KW - 35A10

UR - http://eudml.org/doc/268741

ER -

## References

top- [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 Zbl0176.45203
- [2] L. Nirenberg: “An abstract form of the nonlinear Cauchy-Kowalewski theorem”,J. Differential Geometry, Vol. 6 (1972), pp. 561–576. Zbl0257.35001
- [3] T. Nishida: “A Note On A Theorem Of Nirenberg”,J. Differential Geometry, Vol. 12, (1977), pp. 629–633. Zbl0368.35007
- [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. Zbl0836.35004
- [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.

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