Ordinary Differential Equation - Existence and Uniqueness of Solutions

Existence and Uniqueness of Solutions

There are several theorems that establish existence and uniqueness of solutions to initial value problems involving ODEs both locally and globally. The two main theorems are

Theorem Assumption Conclusion
Peano existence theorem F continuous local existence only
Picard–Lindelöf theorem F Lipschitz continuous local existence and uniqueness

which are both local results.

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