| Title:
|
On the existence and the uniqueness of solutions and on the convergence of successive approximations in the Darboux problem for certain differential equations of the type $u_{x_1\cdots x_n}=f(x_1,\cdots,x_n,u,\cdots,u_{x_{l_1}\cdots x_{l_j}},\cdots)$ (English) |
| Author:
|
Ďurikovič, Vladimír |
| Language:
|
English |
| Journal:
|
Časopis pro pěstování matematiky |
| ISSN:
|
0528-2195 |
| Volume:
|
95 |
| Issue:
|
2 |
| Year:
|
1970 |
| Pages:
|
178-195 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35A05 |
| idZBL:
|
Zbl 0191.11502 |
| idMR:
|
MR0450758 |
| DOI:
|
10.21136/CPM.1970.108350 |
| . |
| Date available:
|
2009-09-23T08:11:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108350 |
| . |
| Reference:
|
[1] W. Walter: Eindeutigkeitssätze für gewòhnliche, parabolische, und hyperbolische Differentialgleichungen.Math. Zeitschrift 74 (3) (1960), pp. 191 - 209. MR 0117427 |
| Reference:
|
[2] M. Kwapisz B. Palczewski, W. Pawelski: Sur ľunicité des solutions de certaines équations différentielles du type $u_{xyz} - f(x, y, z, u, u_x, u_y,u_z, u_{xy}, u_{xz}, u_{yz})$.Ann. Polon. Math. 11 (1961), pp. 75-106. MR 0136880 |
| Reference:
|
[3] B. Palczewski: On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem under the conditions of the Krasnosielski and Krein type.Ann. Polon. Math. 14 (1964), pp. 183-190. Zbl 0132.07301, MR 0161014 |
| Reference:
|
[4] J. S. W. Wong: On the convergence of successive approximations in the Darboux problem.Ann. Polon. Math. 17 (1966), pp. 329-336. Zbl 0144.13704, MR 0188579 |
| Reference:
|
[5] E. R. van Kampen: Notes on systems of ordinary differеntial еquations.Amеrican Journal of Math. 63 (1941), pp. З71-З76. |
| Reference:
|
[6] W. A. J. Luxemburg: On thе convеrgеncе of succеssivе approximàtions in thе thеory of ordinary diffеrеntial еquations II.Indag. Math. 20 (1958), pp. 540-546. MR 0124554 |
| . |
