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:
“Sometimes I think that the biggest difference between men and women is that more men need to seek out some terrible lurking thing in existence and hurl themselves upon it.... Women know where it lives but they can let it alone.”
—Russell Hoban (b. 1925)
“There are in our existence spots of time,”
—William Wordsworth (1770–1850)
“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)
“Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.”
—Isaac Asimov (1920–1992)