# Grönwall's inequality

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In mathematics, **Grönwall's lemma** states the following. If, for , and are continuous functions such that the inequality

holds on , with and positive constants, then

on .

It is named for Thomas Hakon Grönwall (1877-1932).

Grönwall's lemma is an important tool used for obtaining various estimates in ordinary differential equations. In particular, it is used to prove uniqueness of a solution to the initial value problem, see the Picard-Lindelöf theorem.