Ordinary Differential Equation - Existence and Uniqueness of Solutions

Existence and Uniqueness of Solutions

There are several theorems that establish existence and uniqueness of solutions to initial value problems involving ODEs both locally and globally. The two main theorems are

Theorem Assumption Conclusion
Peano existence theorem F continuous local existence only
Picard–Lindelöf theorem F Lipschitz continuous local existence and uniqueness

which are both local results.

Read more about this topic:  Ordinary Differential Equation

Famous quotes containing the words existence, uniqueness and/or solutions:

    Sport in the sense of a mass-spectacle, with death to add to the underlying excitement, comes into existence when a population has been drilled and regimented and depressed to such an extent that it needs at least a vicarious participation in difficult feats of strength or skill or heroism in order to sustain its waning life-sense.
    Lewis Mumford (1895–1990)

    Somehow we have been taught to believe that the experiences of girls and women are not important in the study and understanding of human behavior. If we know men, then we know all of humankind. These prevalent cultural attitudes totally deny the uniqueness of the female experience, limiting the development of girls and women and depriving a needy world of the gifts, talents, and resources our daughters have to offer.
    Jeanne Elium (20th century)

    Football strategy does not originate in a scrimmage: it is useless to expect solutions in a political compaign.
    Walter Lippmann (1889–1974)