Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Understanding uniqueness

  1. Oct 25, 2014 #1
    Hi,

    I was just wondering why taking ∂f/∂y provides the interval on which y is unique (or not necessarily). Could someone possibly provide some mathematical intuition behind this and possibly a proof of some sort detailing why y is unique if ∂f/dy is continuous? Also, how exactly (if it can) is uniqueness determined if ∂f/dy is discontinuous at a certain point?
     
  2. jcsd
  3. Oct 25, 2014 #2
    I'm confused, what do you mean that "y is unique".
     
  4. Oct 25, 2014 #3

    lurflurf

    User Avatar
    Homework Helper

    ^Maybe this question is about The[/PLAIN] [Broken] Picard–Lindelöf theorem?
    link
    http://en.wikipedia.org/wiki/Picard–Lindelöf_theorem

    The theorem gives sufficient conditions so a solution that fails to satisfy the hypothesis might still be unique, but it would need to be shown by a different method. Of course there also might be multiple solutions.

    There should be some discussion of this in most differential equations books.
     
    Last edited by a moderator: May 7, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Understanding uniqueness
  1. Uniqueness Theorem (Replies: 1)

Loading...