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