existence and uniqueness of solution of ordinary differential equations
Let where is an open subset of which is a normed vector space, and let be a continuous differentiable map
Then the ordinary differential equation defined as
with the initial condition
where has a unique solution on some interval containing zero. More specifically there exists such that the following is a unique function
such that and .[HS]
References
- HS Hirsch, W. Morris, Smale, Stephen.: Differential Equations, Dynamical Systems, And Linear Algebra. Academic Press, Inc. New York, 1974.
Title | existence and uniqueness of solution of ordinary differential equations |
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Canonical name | ExistenceAndUniquenessOfSolutionOfOrdinaryDifferentialEquations |
Date of creation | 2013-03-22 13:36:50 |
Last modified on | 2013-03-22 13:36:50 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 13 |
Author | Daume (40) |
Entry type | Theorem |
Classification | msc 35-00 |
Classification | msc 34-00 |
Classification | msc 34A12 |
Related topic | PicardsTheorem2 |
Related topic | CauchyKowalewskiTheorem |