| Title:
|
A note on hyperbolic partial differential equations. II. (English) |
| Author:
|
Rzepecki, Bogdan |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1981 |
| Pages:
|
355-364 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35A35 |
| MSC:
|
35L10 |
| idZBL:
|
Zbl 0571.35065 |
| idMR:
|
MR637964 |
| . |
| Date available:
|
2009-09-25T09:16:26Z |
| Last updated:
|
2012-07-31 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136276 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/132406 |
| . |
| Reference:
|
[1] BIELECKI A. : Une remarque sur la méthode de Banach-Cacciopoli-Tikhonov dans la theorie des équations différentielles ordinaires.Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 4, 1956, 261-264. MR 0082073 |
| Reference:
|
[2] BIELECKI A. : Une remarque sur l'application de la méthode de Banach-Cacciopoli-Tikhonov dans la theorie de l'équation s=f(x, y, z, p, q).Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 4, 1956, 265-268. MR 0082074 |
| Reference:
|
[3] ĎURIKOVlČ V. : On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type uxy = f(x, y, u, ux, uy).Spisy přírodov. fak. Univ. J. E. Purkyně v Brně 4, 1968, 223-236. |
| Reference:
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[4] ĎURIKOVlČ V. : On the existence and uniqueness of solutions and on the convergence of successive aproximations in the Darboux problem for certain differential equations of the type $u_{x_1\cdots x_n}=f(x_1,\cdots,x_n,u,\cdots,u_{x_{l_1}\cdots x_{l_j}},\cdots)$.Čas. pro pěstov. mat. 95, 1970, 178-195 MR 0450758 |
| Reference:
|
[5] ĎURIKOVlČ V. : The convergence of successive approximations for boundary value problems of hyperbolic equations in the Banach space.Mat. Časop. 21, 1971, 33-54. MR 0355387 |
| Reference:
|
[6] GAJEWSKI H., GROGER K., ZACHARIAS K. : Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie-Verlag, Berlin, 1974. MR 0636412 |
| Reference:
|
[7] KOOI O. : Existentie-, einduidigheids- en convergence stellingen in de theore der gewone differential vergelijkingen.Thesis V. U., Amsterdam, 1956. |
| Reference:
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[8] KOOI O. : The method of successive approximations and a uniqueness theorem of Krasnoselskii and Krein in the theory of differential equations.Indag. Math. 20, 1958, 322-327. MR 0098859 |
| Reference:
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[9] KRASNOSELSKII M. A. : Two remarks on the method of successive approximations.Uspehi Mat. Nauk 10, 1955, 123-127 [in Russian]. MR 0068119 |
| Reference:
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[10] KRASNOSELSKII M. A., KREIN S. G. : On a class of uniqueness theorems for the equation y'=f(t,y).Uspehi Mat. Nauk 11, 1956, 206-213 [in Russian]. MR 0079152 |
| Reference:
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[11] KRATOWSKI C. : Topologie. V. I.Warszawa, 1952. |
| Reference:
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[12] LUXEMBURG W. A. J. : On the convergence of successive approximations in the theory of ordinary differential equations II.Indag. Math. 20, 1958, 540-546. Zbl 0084.07703, MR 0124554 |
| Reference:
|
[13] LUXEMBURG W. A. J. : On the convergence of successive approximations in the theory of ordinary differential equations III.Nieuw Archief Voor Wiskunde 6, 1958, 93-98. Zbl 0085.30201, MR 0124555 |
| Reference:
|
[14] PALCZEWSKI B., PAWELSKI W. : Some remarks on the uniqueness of solutions of the Darboux problem with conditions of the Krasnosielski-Krein type.Ann. Polon. Math. 14, 1964, 97-100. Zbl 0132.07208, MR 0161013 |
| Reference:
|
[15] ROSENBLATT A. : Über die Existenz von Integralen gewöhnlichen Differentialglechungen.Archiv for Mathem. Astr. och Fysik 5 (2), 1909, 1-4. |
| Reference:
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[16] RZEPECKI B. : A generalization of Banach's contraction theorem.Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 26, 1978, 603-609. Zbl 0421.47032, MR 0515618 |
| Reference:
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[17] RZEPECKI B. : Note on the differential equation F(f, y(t), y(h(t)), y'(t)) = 0.Comment. Math. Univ. Carolinae 19, 1978, 627-637. MR 0518176 |
| Reference:
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[18] RZEPECKI B. : Note on hyperbolic partial differential equations I.Mathematica Slovaca 31, 1981, 243-250. MR 0621915 |
| Reference:
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[19] WONG J. S. W. : On the convergence of successive approximations in the Darboux problem.Ann. Polon. Math. 17, 1966, 329-336. Zbl 0144.13704, MR 0188579 |
| . |
