Geodesic
A note on existence theorem of Peano
Archivum mathematicum, Tome 47 (2011) no. 2, pp. 83-89
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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.
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.
Classification : 34A12
Keywords: Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; IVP; ODE; Cauchy problem 
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Zubelevich, Oleg. A note on existence theorem of Peano. Archivum mathematicum, Tome 47 (2011) no. 2, pp. 83-89. http://geodesic.mathdoc.fr/item/ARM_2011_47_2_a1/

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