Request resources to understand Picard–Lindelöf for ODEs

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SUMMARY

The forum discussion centers on the confusion surrounding the Picard–Lindelöf theorem in the context of ordinary differential equations (ODEs). The original poster (OP) seeks additional resources to clarify their understanding, particularly regarding the theorem's converse. The moderator suggests that the OP may be confusing the theorem with Okamura's uniqueness theorem, which provides necessary conditions for the existence of a unique solution to an ODE. The discussion highlights the abundance of online resources available for studying the Picard–Lindelöf theorem and its implications.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with the Picard–Lindelöf theorem
  • Knowledge of Okamura's uniqueness theorem
  • Basic research skills for locating academic resources online
NEXT STEPS
  • Research the proofs and applications of the Picard–Lindelöf theorem
  • Study Okamura's uniqueness theorem and its implications in ODEs
  • Explore online academic resources and textbooks on differential equations
  • Engage with forums or study groups focused on advanced calculus and differential equations
USEFUL FOR

Students and researchers in mathematics, particularly those studying differential equations, as well as educators seeking to clarify the concepts surrounding the Picard–Lindelöf theorem and its applications.

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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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