Peano existence theorem, Non-Lipschitz nonlinearity, non- uniqueness, IVP, ODE, Cauchy problem. Partially supported by grants RFBR , Science. Uniqueness Theorem. 6. Continuity. 8. Existence Theorem. Local Existence Theorem and The Peano Theorem. Local Existence. It should be noted that the Cauchy-Picard existence theorem as well as its proof Key words and phrases: Peano existence theorem, non-Lipschitz nonlinearity, .
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I do not feel confident with this proof because I did not use Ascoli-Arzela, which is used in the typical proof of Peano’s Existence Theorem.
These exist because of the Weierstrass’ theorem. Here is an extract of a work I did for University.
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I don’t think that I can include all the details here without making a huge answer. Thus, do check the link at the end for notations or concepts you don’t fully understand. I commit myself to maintain the link. The proof of Peano theorem will be done using Weierstrass approximation theorem.
A good account of the different approaches that have been followed to prove this theorem can be existencce in Flett’s Differential Analysis.
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Ordinary Differential Equations/Peano’s theorem
Javier 1, 2 11 Dragonite 1, 4 Let’s first consider the scalar case. This concludes the vector setting and the proof.
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Peano existence theorem – Wikiwand
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