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If a differential equation is Lipschitz continuous, then the solution is unique. But what about the implication in the other direction? I know that uniqueness does not imply Lipschitz continuity. But is there a counterexample? A differential equation that is not L-continuous, still the solution is unique?

I would really like to know the answer to this question.

Thank you all for your help,

Hendrik

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# Lipschitz Continuity and Uniqueness

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