# Generic properties of generalized hyperbolic partial differential equations

Annales Polonici Mathematici (1994)

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

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topDariusz 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

top- [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] 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] T. Costello, Generic properties of differential equations, SIAM J. Math. Anal. 4 (1973), 245-249. Zbl0225.35064
- [4] G. Darbo, Punti uniti in transformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 84-92. Zbl0064.35704
- [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] K. Goebel, Thickness of sets in metric spaces and its application in fixed point theory, habilitation thesis, Lublin, 1970 (in Polish).
- [7] P. Hartman and A. Wintner, On hyperbolic partial differential equations, Amer. J. Math., 74 (1952), 834-864. Zbl0048.33302
- [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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