existence and uniqueness of solution of ordinary differential equations
Let E⊂W where E is an open subset of W which is a normed vector space, and let f be a continuous differentiable map
f:E→W. |
Then the ordinary differential equation defined as
˙x=f(x) |
with the initial condition
x(0)=x0 |
where x0∈E has a unique solution on some interval containing zero. More specifically there exists α>0 such that the following is a unique function
x:(-α,α)→E |
such that ˙x=f∘x and x(0)=x0.[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 |
---|---|
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 |