12-267/Existence And Uniqueness Theorem: Difference between revisions
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Revision as of 19:20, 12 October 2012
Disclamer: This is a student prepared note based on the lecure of Monday September 21st.
Def. is called Lipschitz if (a Lipschitz constant of f) such that .
Note that any function that is Lipschitz is uniformly continuous, and that if a function f and its derivative are both continous on a compact set then f is Lipschitz.
Thm. Existence and Uniqueness Theorem for ODEs
Let be continuous and uniformly Lipschitz relative to y. Then the equation with has a unique solution where where M is a bound of f on .