Generic properties of generalized hyperbolic partial differential equations

Dariusz Bielawski

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 2, page 107-115
  • ISSN: 0066-2216

Abstract

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The existence and uniqueness of solutions and convergence of successive approximations are considered as generic properties for generalized hyperbolic partial differential equations with unbounded right-hand sides.

How to cite

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Dariusz Bielawski. "Generic properties of generalized hyperbolic partial differential equations." Annales Polonici Mathematici 59.2 (1994): 107-115. <http://eudml.org/doc/262325>.

@article{DariuszBielawski1994,
abstract = {The existence and uniqueness of solutions and convergence of successive approximations are considered as generic properties for generalized hyperbolic partial differential equations with unbounded right-hand sides.},
author = {Dariusz Bielawski},
journal = {Annales Polonici Mathematici},
keywords = {Darboux problem; generic property; existence and uniqueness of solutions; Bielecki's norms; generic properties},
language = {eng},
number = {2},
pages = {107-115},
title = {Generic properties of generalized hyperbolic partial differential equations},
url = {http://eudml.org/doc/262325},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Dariusz Bielawski
TI - Generic properties of generalized hyperbolic partial differential equations
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 2
SP - 107
EP - 115
AB - The existence and uniqueness of solutions and convergence of successive approximations are considered as generic properties for generalized hyperbolic partial differential equations with unbounded right-hand sides.
LA - eng
KW - Darboux problem; generic property; existence and uniqueness of solutions; Bielecki's norms; generic properties
UR - http://eudml.org/doc/262325
ER -

References

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  1. [1] A. Alexiewicz and W. Orlicz, Some remarks on the existence and uniqueness of solutions of hyperbolic equations z x y = f ( x , y , z , z x , z y ) , Studia Math. 15 (1956), 201-215. Zbl0070.09204
  2. [2] A. Bielecki, Une remarque sur l'application de la méthode de Banach-Caccioppoli-Tikhonov dans la théorie de l'équation s = f(x,y,z,p,q), Bull. Acad. Polon. Sci. Cl. III 4 (1956), 265-268. Zbl0070.09004
  3. [3] T. Costello, Generic properties of differential equations, SIAM J. Math. Anal. 4 (1973), 245-249. Zbl0225.35064
  4. [4] G. Darbo, Punti uniti in transformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 84-92. Zbl0064.35704
  5. [5] F. S. De Blasi and J. Myjak, Generic properties of hyperbolic partial differential equations, J. London Math. Soc. (2) 15 (1977), 113-118. Zbl0353.35064
  6. [6] K. Goebel, Thickness of sets in metric spaces and its application in fixed point theory, habilitation thesis, Lublin, 1970 (in Polish). 
  7. [7] P. Hartman and A. Wintner, On hyperbolic partial differential equations, Amer. J. Math., 74 (1952), 834-864. Zbl0048.33302
  8. [8] A. Lasota and J. Yorke, The generic property of existence of solutions of differential equations in Banach space, J. Differential Equations 13 (1973), 1-12. Zbl0259.34070

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