Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I was wondering if anyone knew of a legitimate citable reference where Picard's Theorem on the existence of solutions to ODEs in Banach space is proven? For some reason I can only find proofs for the case of $\mathbb{R}^n$ in any of the books I have looked at. I realize that the proof is the same, but I would like to have a reference where I do not have to mention this fact.

Thanks in advance

share|cite|improve this question

1 Answer 1

up vote 2 down vote accepted

Try Theorem 6, pp.117-118 of the survey paper

Lobanov, S. G. & Smolyanov, O. G. "Ordinary differential equations in locally convex spaces". Uspekhi Mat. Nauk, 1994, 49, 93-168

(link to paper). It being partially a survey paper, the theorem is stated without proof; if you want the proofs, you'd have to follow the references therein.

share|cite|improve this answer
Thank you very much. –  user12014 Jun 6 '12 at 10:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.