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:
“Suppose that humans happen to be so constructed that they desire the opportunity for freely undertaken productive work. Suppose that they want to be free from the meddling of technocrats and commissars, bankers and tycoons, mad bombers who engage in psychological tests of will with peasants defending their homes, behavioral scientists who can’t tell a pigeon from a poet, or anyone else who tries to wish freedom and dignity out of existence or beat them into oblivion.”
—Noam Chomsky (b. 1928)
“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)
“Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.”
—Isaac Asimov (1920–1992)