Several Notes on Existence Theorem of Peano

MR2976044 Oleg ZUBELEVICH Oleg ZUBELEVICH Several Notes on Existence Theorem of Peano Funkcialaj Ekvacioj. Serio Internacia 55 2012 89--97 http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-1/55_89.pdf http://www.ams.org/mathscinet-getitem?mr=MR2976044 An ODE in conditions of Peano's theorem has been considered. A family of solutions with Borel measurable dependence of the initial data has been obtained. Corresponding existence theorem for the transport equation has been proved. Peano existence theorem, Non-Lipschitz nonlinearity, Non-uniqueness, IVP, ODE, Cauchy problem. 34A12. 55-89 2012 Several Notes on Existence Theorem of Peano Oleg ZUBELEVICH Oleg ZUBELEVICH 1 Edwards, R. Functional Analysis. Theory and Applications Holt, Rinehart and Winston, London 1965 MR0221256 2 Bogachev, V. Measure Theory, Vol. II Springer-Verlag, Berlin 2007 MR2267655 3 Bownds, M. A Uniqueness Theorem for Non-Lipschitzian Systems of Ordinary Differential Equations Funkcial. Ekvac. 13 1970 61-65 MR0293150 0293150

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