On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type u x y = f ( x , y , u , u x , u y )

Vladimír Ďurikovič

Archivum Mathematicum (1968)

  • Volume: 004, Issue: 4, page 223-235
  • ISSN: 0044-8753

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Ďurikovič, Vladimír. "On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type $u_{xy}=f(x,y,u,u_x,u_y)$." Archivum Mathematicum 004.4 (1968): 223-235. <http://eudml.org/doc/15847>.

@article{Ďurikovič1968,
author = {Ďurikovič, Vladimír},
journal = {Archivum Mathematicum},
language = {eng},
number = {4},
pages = {223-235},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type $u_\{xy\}=f(x,y,u,u_x,u_y)$},
url = {http://eudml.org/doc/15847},
volume = {004},
year = {1968},
}

TY - JOUR
AU - Ďurikovič, Vladimír
TI - On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type $u_{xy}=f(x,y,u,u_x,u_y)$
JO - Archivum Mathematicum
PY - 1968
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 004
IS - 4
SP - 223
EP - 235
LA - eng
UR - http://eudml.org/doc/15847
ER -

References

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  1. Kampen van E. R., Notes on systems of ordinary differential equations, American Journal of Math. 63 (1941), pp. 371-376. (1941) MR0003896
  2. Luxemburg W. A. J., On the convergence of successive approximations in the theory of ordinary differential equations II, Indag. Math. 20 (1958), pp. 540-546. (1958) Zbl0084.07703MR0124554
  3. Luxemburg W. A. J., On the convergence of successive approximations in the theory of ordinary differential equations III, Nieuw Archief voor Wiskunde (3), VI (1958), pp. 93-98. (1958) Zbl0085.30201MR0124555
  4. Palczewski B., On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem under the conditions of the Krasnosilski and Krein type, Ann. polon. Math. 14 (1964), pp. 183-190. (1964) MR0161014
  5. Ф. Tpикоми, Лекции пo ypaвнениям в частых производных, Mocквa 1957, pp 205-216. (1957) 
  6. Wong J. S. W., On the convergence of successive approximations in the Darboux problem, Ann. Polon. Math. XVII (1966), pp. 329-336. (1966) Zbl0144.13704MR0188579
  7. Wong J. S. W., Remarks on uniqueness theorem of solutions of the Darboux problem, Canad. Math. Bull. 8 (1965), pp. 791-796. (1965) MR0193378

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