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Keywords:
Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; IVP; ODE; Cauchy problem
Peano existence theorem; non-Lipschitz nonlinearity; non-uniqueness; IVP; ODE; Cauchy problem
Summary:
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.
References:
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