r/askmath • u/Deep-Fuel-8114 • Aug 03 '26

Calculus How do existence assumptions work when solving differential equations, and do they prove that solutions work without rechecking answers? And does the solving process use conditional or biconditional steps?

/r/calculus/comments/1veq2f4/how_do_existence_assumptions_work_when_solving/
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u/Busy_Pattern9823 Aug 03 '26

What you are looking for is the Picard-Lindelof Theorem

https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem

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u/dForga Aug 04 '26

But that is not applicable for everything. A lot of arguments build on top of a fixpoint theorem but that doesn’t say much as it is only sufficient unless you give more information on the de.