# Peano’s theorem

If

 $\displaystyle\frac{dy}{dx}$ $\displaystyle=$ $\displaystyle f(x,y)$ (1)

is an ordinary differential equation where $f(x,y)$ is continuous on a planar domain $E$, then (1) has at least one integral curve for each $(x_{0},y_{0})$ of $E$.[KF, T]

## References

• KF Kolmogorov, A.N. & Fomin, S.V., Introductory Real Analysis, Translated & Edited by Richard A. Silverman, Dover Publications, Inc. New York, 1970.
• T Teschl, Gerald, http://www.mat.univie.ac.at/ gerald/ftp/book-ode/index.htmlhttp://www.mat.univie.ac.at/ gerald/ftp/book-ode/index.html, 2004.
Title Peano’s theorem PeanosTheorem 2013-03-22 15:20:21 2013-03-22 15:20:21 Daume (40) Daume (40) 6 Daume (40) Theorem msc 34A12