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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In particular, the objections made by user made sense to me ;eano that time and I won’t repeat them here. Thank you in advance for helping me finding the possible error. Post as a guest Name. Rether 4 This is the point which I am less sure of.

## Oh no, there’s been an error

Sign up or log in Sign up using Google. Rugh Sep 1 ’16 at I am not sure the proof is wrong or correct; however here are is one unwarranted conclusions that is drawn.

These exist because of the Weierstrass’ theorem. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Email Thelrem, but never shown. Let’s write this solution: I don’t know if you agree with me in this point but it was the feeling I got first time I read your question.

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This is a theorem of elementary analysis: A good account of the different approaches that have been followed to prove this theorem can be found in Flett’s Differential Analysis.

Javier 1, 2 11 In particular, the idea rheorem using Weierstrass approximation can be attributed to Romanian mathematician Constantin Corduneanu. I haven’t considered the latter as a duplicate for this reason. The argument you use that “globally Lipshitz etc” is not quite correct. This concludes the vector setting and the proof.

### NPTEL :: Mathematics – Ordinary Differential Equations and Applications

Dragonite 1, 4 I am looking for proof verification of the following and any suggestions for improvement. After that your argument works to show that the limit of the subsequence verifies the ode. 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.

This completes the proof of the scalar case.

Rether Sep 1 eistence at By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Here is an extract of a work I did for University.

You can check my answer there as well as the linked document that contains the notations that may be strange and other details.

Cauchu exist because of the Weiertrass theorem. I suspect that the following proof, which doesn’t, is therefore wrong. Luckily enough because you can’t get that from Ascoli. I don’t see that hold. To check that this does or does not happen you need to unpack the proof of existence and uniqueness and see if you can guarantee a lower bound to the width of the existence-uniqueness intervals.

I don’t think that I can include all the details here without making a huge answer.

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Sign up using Email and Password. The solution may leave that rectangle.