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 ⋯ x n = f ( x 1 , ⋯ , x n , u , ⋯ , u x l 1 ⋯ x l j , ⋯ )

Vladimír Ďurikovič

Časopis pro pěstování matematiky (1970)

  • Volume: 095, Issue: 2, page 178-195
  • ISSN: 0528-2195

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Ďurikovič, Vladimír. "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 $u_{x_1\cdots x_n}=f(x_1,\cdots ,x_n,u,\cdots ,u_{x_{l_1}\cdots x_{l_j}},\cdots )$." Časopis pro pěstování matematiky 095.2 (1970): 178-195. <http://eudml.org/doc/19180>.

@article{Ďurikovič1970,
author = {Ďurikovič, Vladimír},
journal = {Časopis pro pěstování matematiky},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {178-195},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
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 $u_\{x_1\cdots x_n\}=f(x_1,\cdots ,x_n,u,\cdots ,u_\{x_\{l_1\}\cdots x_\{l_j\}\},\cdots )$},
url = {http://eudml.org/doc/19180},
volume = {095},
year = {1970},
}

TY - JOUR
AU - Ďurikovič, Vladimír
TI - 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 $u_{x_1\cdots x_n}=f(x_1,\cdots ,x_n,u,\cdots ,u_{x_{l_1}\cdots x_{l_j}},\cdots )$
JO - Časopis pro pěstování matematiky
PY - 1970
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 095
IS - 2
SP - 178
EP - 195
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/19180
ER -

References

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  1. W. Walter, Eindeutigkeitssätze für gewòhnliche, parabolische, und hyperbolische Differentialgleichungen, Math. Zeitschrift 74 (3) (1960), pp. 191 - 209. (1960) MR0117427
  2. M. Kwapisz B. Palczewski, W. Pawelski, Sur ľunicité des solutions de certaines équations différentielles du type u x y z - f ( x , y , z , u , u x , u y , u z , u x y , u x z , u y z ) , Ann. Polon. Math. 11 (1961), pp. 75-106. (1961) MR0136880
  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. (1964) Zbl0132.07301MR0161014
  4. J. S. W. Wong, On the convergence of successive approximations in the Darboux problem, Ann. Polon. Math. 17 (1966), pp. 329-336. (1966) Zbl0144.13704MR0188579
  5. E. R. van Kampen, Notes on systems of ordinary differеntial еquations, Amеrican Journal of Math. 63 (1941), pp. З71-З76. (1941) 
  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. (1958) MR0124554

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