A note on hyperbolic partial differential equations. II.

Bogdan Rzepecki

Mathematica Slovaca (1981)

  • Volume: 31, Issue: 4, page 355-364
  • ISSN: 0232-0525

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Rzepecki, Bogdan. "A note on hyperbolic partial differential equations. II.." Mathematica Slovaca 31.4 (1981): 355-364. <http://eudml.org/doc/34114>.

@article{Rzepecki1981,
author = {Rzepecki, Bogdan},
journal = {Mathematica Slovaca},
keywords = {fixed point theorems; existence; continuous dependence; Darboux problem; initial functions},
language = {eng},
number = {4},
pages = {355-364},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A note on hyperbolic partial differential equations. II.},
url = {http://eudml.org/doc/34114},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Rzepecki, Bogdan
TI - A note on hyperbolic partial differential equations. II.
JO - Mathematica Slovaca
PY - 1981
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 31
IS - 4
SP - 355
EP - 364
LA - eng
KW - fixed point theorems; existence; continuous dependence; Darboux problem; initial functions
UR - http://eudml.org/doc/34114
ER -

References

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  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. (1956) MR0082074
  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. (1968) 
  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 x n = f ( x 1 , , x n , u , , u x l 1 x l j , ) , Čas. pro pěstov. mat. 95, 1970, 178-195 (1970) MR0450758
  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. (1971) MR0355387
  6. GAJEWSKI H., GROGER K., ZACHARIAS K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974. (1974) MR0636412
  7. KOOI O., Existentie-, einduidigheids- en convergence stellingen in de theore der gewone differential vergelijkingen, Thesis V. U., Amsterdam, 1956. (1956) 
  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. (1958) MR0098859
  9. KRASNOSELSKII M. A., Two remarks on the method of successive approximations, Uspehi Mat. Nauk 10, 1955, 123-127 [in Russian]. (1955) MR0068119
  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]. (1956) MR0079152
  11. KRATOWSKI C., Topologie. V. I, Warszawa, 1952. (1952) 
  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. (1958) Zbl0084.07703MR0124554
  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. (1958) Zbl0085.30201MR0124555
  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. (1964) Zbl0132.07208MR0161013
  15. ROSENBLATT A., Über die Existenz von Integralen gewöhnlichen Differentialglechungen, Archiv for Mathem. Astr. och Fysik 5 (2), 1909, 1-4. (1909) 
  16. RZEPECKI B., A generalization of Banach's contraction theorem, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 26, 1978, 603-609. (1978) Zbl0421.47032MR0515618
  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. (1978) MR0518176
  18. RZEPECKI B., Note on hyperbolic partial differential equations I, Mathematica Slovaca 31, 1981, 243-250. (1981) MR0621915
  19. WONG J. S. W., On the convergence of successive approximations in the Darboux problem, Ann. Polon. Math. 17, 1966, 329-336. (1966) Zbl0144.13704MR0188579

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