Request resources to understand Picard–Lindelöf for ODEs

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Discussion Overview

The discussion revolves around the Picard–Lindelöf theorem related to ordinary differential equations (ODEs), specifically focusing on the confusion regarding its converse and the request for additional resources to understand the topic better.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion about the converse of the Picard–Lindelöf theorem and seeks additional reading materials.
  • Another participant questions the nature of the confusion, asking for clarification on what the converse is thought to be and for examples of the confusion experienced.
  • A different participant suggests that the converse may refer to a necessary condition for uniqueness, mentioning Okamura's theorem as a related concept.
  • Several participants express skepticism about the original poster's engagement, with comments suggesting they may not be actively participating in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of the confusion regarding the Picard–Lindelöf theorem, and the discussion remains unresolved with multiple viewpoints presented.

Contextual Notes

There are limitations in the clarity of the original poster's question, as well as the lack of specific examples or definitions provided, which may affect the ability to address their confusion adequately.

adf89812
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I always confuse picard-lindelof forints converse. I want additional reading but don't know how to find it.

Moderator Note: Moved from Academic Advising since it is too specific, and too narrow for Science Textbooks.
 
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You confuse Picard-Lindelöf with what? Hungarian money? And what are you looking for? The internet is full of proofs of Picard-Lindelöf.
 
Last edited:
So that we can help you with this, can you post here:
  1. what you think is the converse of the Picard–Lindelöf theorem?
  2. an example of where you have had this confusion?
 
Since Picard-Lindelof gives a sufficient condition for the existence of a unique solution to an ODE, perhaps by a converse you mean a necessary condition. Such a condition is called Okamura's (uniqueness) theorem, which you can search online.
 
This poster just creates threads and never replies back. Not sure if its a bot.
 
MidgetDwarf said:
This poster just creates threads and never replies back. Not sure if its a bot.
Agreed. OP is on a temporary vacation from PF, and this thread is now locked. Thanks all for trying to help the OP with their question.
 
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