A note on existence theorem of Peano

Oleg Zubelevich

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 2, page 83-89
  • ISSN: 0044-8753

Abstract

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An ODE with non-Lipschitz right hand side has been considered. A family of solutions with L p -dependence of the initial data has been obtained. A special set of initial data has been constructed. In this set the family is continuous. The measure of this set has been estimated.

How to cite

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Zubelevich, Oleg. "A note on existence theorem of Peano." Archivum Mathematicum 047.2 (2011): 83-89. <http://eudml.org/doc/116536>.

@article{Zubelevich2011,
abstract = {An ODE with non-Lipschitz right hand side has been considered. A family of solutions with $L^p$-dependence of the initial data has been obtained. A special set of initial data has been constructed. In this set the family is continuous. The measure of this set has been estimated.},
author = {Zubelevich, Oleg},
journal = {Archivum Mathematicum},
keywords = {Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; IVP; ODE; Cauchy problem; Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; Cauchy problem},
language = {eng},
number = {2},
pages = {83-89},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on existence theorem of Peano},
url = {http://eudml.org/doc/116536},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Zubelevich, Oleg
TI - A note on existence theorem of Peano
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 2
SP - 83
EP - 89
AB - An ODE with non-Lipschitz right hand side has been considered. A family of solutions with $L^p$-dependence of the initial data has been obtained. A special set of initial data has been constructed. In this set the family is continuous. The measure of this set has been estimated.
LA - eng
KW - Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; IVP; ODE; Cauchy problem; Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; Cauchy problem
UR - http://eudml.org/doc/116536
ER -

References

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  11. Levy, P., Provessus stochastiques et mouvement Brownien, Gauthier–Villars, Paris, 1948. (1948) MR0190953
  12. Ramankutty, P., Kamke’s uniqueness theorem, J. London Math. Soc. (2) 22 (1982), 110–116. (1982) MR0579814
  13. Schwartz, L., Analyse mathèmatique, Herman, 1967. (1967) Zbl0171.01301
  14. Sobolevskii, S. L., 10.1023/A:1016038732103, Differential Equations 38 (3) (2002), 451–452. (2002) MR2005086DOI10.1023/A:1016038732103
  15. Szep, A., Existence theorem for weak solutions for ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungar. 6 (1971), 197–203. (1971) MR0330688
  16. Yorke, J. A., A continuous differential equation in Hilbert space without existence, Funkcial. Ekvac. 13 (1970), 19–21. (1970) Zbl0248.34061MR0264196

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