Abstract version of the Cauchy-Kowalewski problem
Oleg Zubelevich
Open Mathematics, Tome 2 (2004), p. 382-387 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:268741
@article{bwmeta1.element.doi-10_2478_BF02475235,
     author = {Oleg Zubelevich},
     title = {Abstract version of the Cauchy-Kowalewski problem},
     journal = {Open Mathematics},
     volume = {2},
     year = {2004},
     pages = {382-387},
     zbl = {1064.35005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475235}
}
Oleg Zubelevich. Abstract version of the Cauchy-Kowalewski problem. Open Mathematics, Tome 2 (2004) pp. 382-387. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475235/

[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 | Zbl 0176.45203

[2] L. Nirenberg: “An abstract form of the nonlinear Cauchy-Kowalewski theorem”,J. Differential Geometry, Vol. 6 (1972), pp. 561–576. | Zbl 0257.35001

[3] T. Nishida: “A Note On A Theorem Of Nirenberg”,J. Differential Geometry, Vol. 12, (1977), pp. 629–633. | Zbl 0368.35007

[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. | Zbl 0836.35004

[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.