Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there any proof which would show that the uniqueness theorem does not imply complete uniqueness of a ODE solution?

Would it have any relation between the interval where uniqueness is assumed to exist and the maximal interval of existence?

Thanks :)

share|cite|improve this question
Did you mean as in Theorem 2.4.1 or somethings else?. Regards – Amzoti Feb 15 '13 at 23:46

The usual example is something along the lines of $$ y' = 2 \sqrt y, \; \; y(0) = 0. $$ Then two legitimate solutions for $x \geq 0$ are $$ y = 0 $$ OR $$ y = x^2. $$

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.