In mathematics, Grönwall's lemma states the following. If, for , and are continuous functions such that the inequality Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ... For the socioeconomic meaning, see social inequality. ...

holds on , with K and L 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. In mathematics, and in particular analysis, an ordinary differential equation (or ODE) is an equation that involves the derivatives of an unknown function of one variable. ... In predicate logic and technical fields that depend on it, uniqueness quantification, or unique existential quantification, is an attempt to formalise the notion of something being true for exactly one thing, or exactly one thing of a certain type. ... In mathematics, an initial value problem is a statement of a differential equation together with specified value of the unknown function at a given point in the domain of the solution. ... In mathematics, the Picard-Lindelöf theorem on existence and uniqueness of solutions of differential equations ( Picard 1890, Lindelöf 1894) states that an initial value problem has exactly one solution if f is Lipschitz continuous in , continuous in as long as stays bounded. ...

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