• Title: Picard–Lindelöf Theorem

• Series: Ordinary Differential Equations

• Chapter: Uniqueness and Existence of Solutions

• YouTube-Title: Ordinary Differential Equations 12 | Picard–Lindelöf Theorem

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• Related videos:

  • Real Analysis 31 | Uniform Limits of Continuous Functions are Continuous
• Timestamps

  00:00 Introduction

  00:51 Initial value problem

  01:12 Assumption: locally Lipschitz continuous function

  01:48 Banach fixed-point theorem

  02:18 Define metric space and contraction

  03:51 Function Space X

  04:43 Correction: codomain of α has to be changed, see PDF

  07:39 Complete metric function space

  08:10 Check the contraction

  12:08 Correction: new codomain of α needed, see PDF

  12:53 Make epsilon small enough

  13:09 Picard-Lindelöf theorem

  14:26 Credits

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• Last update: 2026-04

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