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 and, existence, uniqueness and/or solutions:
“For it is only as an aesthetic phenomenon that existence and the world are eternally justified.”
—Friedrich Nietzsche (1844–1900)
“All that makes existence valuable to any one depends on the enforcement of restraints upon the actions of other people.”
—John Stuart Mill (1806–1873)
“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)
“Every man is in a state of conflict, owing to his attempt to reconcile himself and his relationship with life to his conception of harmony. This conflict makes his soul a battlefield, where the forces that wish this reconciliation fight those that do not and reject the alternative solutions they offer. Works of art are attempts to fight out this conflict in the imaginative world.”
—Rebecca West (1892–1983)