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:
“Nothing exists except by virtue of a disequilibrium, an injustice. All existence is a theft paid for by other existences; no life flowers except on a cemetery.”
—Rémy De Gourmont (1858–1915)
“Until now when we have started to talk about the uniqueness of America we have almost always ended by comparing ourselves to Europe. Toward her we have felt all the attraction and repulsions of Oedipus.”
—Daniel J. Boorstin (b. 1914)
“Football strategy does not originate in a scrimmage: it is useless to expect solutions in a political compaign.”
—Walter Lippmann (1889–1974)