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.
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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.
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
This completes the proof of the scalar case.
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.
Sign up using Email and Password. The solution may leave that rectangle.