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:
“We go on dating from Cold Fridays and Great Snows; but a little colder Friday, or greater snow would put a period to man’s existence on the globe.”
—Henry David Thoreau (1817–1862)
“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)
“The anorexic prefigures this culture in rather a poetic fashion by trying to keep it at bay. He refuses lack. He says: I lack nothing, therefore I shall not eat. With the overweight person, it is the opposite: he refuses fullness, repletion. He says, I lack everything, so I will eat anything at all. The anorexic staves off lack by emptiness, the overweight person staves off fullness by excess. Both are homeopathic final solutions, solutions by extermination.”
—Jean Baudrillard (b. 1929)