# Peano theorem

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One of the existence theorems for solutions of an ordinary differential equation (cf. Differential equation, ordinary), established by G. Peano , and consisting in the following. Suppose one is given the differential equation (*)

If the function is bounded and continuous in a region , then through each interior point of this region there passes at least one integral curve for (*). It may be that more than one integral curve passes through a certain point, e.g. for the equation there exists an infinite set of integral curves passing through :   where and are arbitrary constants.

There are generalizations (including multi-dimensional ones) of Peano's theorem (see , ).

How to Cite This Entry:
Peano theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Peano_theorem&oldid=14971
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article