Peano’s theorem
If
$\frac{dy}{dx}$ | $=$ | $f(x,y)$ | (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 |
---|---|
Canonical name | PeanosTheorem |
Date of creation | 2013-03-22 15:20:21 |
Last modified on | 2013-03-22 15:20:21 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 6 |
Author | Daume (40) |
Entry type | Theorem |
Classification | msc 34A12 |