existence and uniqueness of solution of ordinary differential equations


Let EW where E is an open subset of W which is a normed vector spacePlanetmathPlanetmath, and let f be a continuous differentiable map

f:EW.

Then the ordinary differential equationMathworldPlanetmath defined as

x˙=f(x)

with the initial conditionMathworldPlanetmath

x(0)=x0

where x0E 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˙=fx and x(0)=x0.[HS]

References

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