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, .
|Published (Last):||3 April 2018|
|PDF File Size:||20.13 Mb|
|ePub File Size:||4.35 Mb|
|Price:||Free* [*Free Regsitration Required]|
Ordinary Differential Equations/Peano’s theorem – Wikibooks, open books for an open world
I am not sure the proof is wrong or correct; however here are is one unwarranted conclusions that is drawn. Post as a guest Name.
Thus, do check the existencw at the end for notations or concepts you don’t fully understand. Sign up using Facebook. These exist because of the Weiertrass theorem. I think that one of the major problems proof-verifying your question is that there are missing details.
Peano existence theorem
Let’s first consider the scalar case. A good account of the different approaches that have been followed to prove this theorem can be found in Flett’s Differential Analysis. In particular, the objections made by user made sense to me at that time and Existende won’t repeat them here.
Rugh Sep 1 ’16 at Sign up using Facebook. I am looking for proof verification of the following and any suggestions for improvement.
Let’s write this solution: Rether Sep 1 ’16 at The argument you use that “globally Lipshitz etc” is not quite correct. Luckily enough because you can’t get that from Ascoli. Home Questions Tags Users Unanswered. Sign up or log in Sign up using Google. I don’t think that I can include all the details here without making a huge answer. I commit myself to maintain the link. existenec
NPTEL :: Mathematics – Ordinary Differential Equations and Applications
This completes the proof of the scalar case. Email Required, but never shown. This is a theorem of elementary analysis: After that your argument works to show that the limit of the subsequence verifies the ode.
I suspect that the following proof, which doesn’t, is therefore wrong. Rether 4 I don’t pfano that hold. Sign up or log in Sign up using Google. The proof of Peano theorem will be done using Weierstrass approximation theorem. Thank you in advance for helping me finding the possible error.
Oh no, there’s been an error