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 am looking for proof verification of the following and any suggestions for improvement. I suspect that the following proof, which doesn’t, is therefore wrong. Rether 4 The proof of Peano theorem will be done using Weierstrass approximation theorem.

For this Ascoli helps a lot.

I commit myself to maintain the link. Sign up or log in Sign up using Google. Sign up using Email and Password. By clicking “Post Your Answer”, you acknowledge theorej you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Email Required, but never shown. In particular, the objections made by user made sense to me at that time and I won’t repeat them here. Here is an penao of a work I did for University.

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Javier 1, 2 11 This concludes the vector setting and the proof.

Dragonite 1, 4 To check that this does or does not happen you need to unpack the proof of existence and uniqueness and theroem if you can guarantee a lower bound to the width of the existence-uniqueness intervals. Let’s write this solution: Post as a guest Name. Home Questions Tags Users Unanswered.

These exist because of the Weiertrass theorem. This is a theorem of elementary analysis: Rether Sep 1 ’16 at Sign up using Facebook. Luckily enough because you can’t get that from Ascoli.

Ordinary Differential Equations/Peano’s theorem

Sign up using Facebook. In particular, the idea of using Weierstrass approximation can be attributed to Romanian mathematician Constantin Corduneanu.

After that your argument works to show that the limit of the subsequence verifies the ode. The argument you use that “globally Lipshitz etc” is not quite correct. I haven’t considered the latter as a duplicate for this reason.

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Javier 1, 2 11 Theofem is the point which I am less sure of. Home Questions Tags Users Unanswered. Mathematics Stack Exchange works best with JavaScript enabled.

NPTEL :: Mathematics – Ordinary Differential Equations and Applications

Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Sign up using Email and Password. 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.

Post as a guest Name. The solution may leave that rectangle. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.