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What is Picard-Lindelof Theorem Explained about?
This document presents the Picard-Lindelof theorem, which states that an ordinary differential equation has a unique solution if the operator defined by the equation is a contraction mapping on a complete metric space. The proof involves several lemmas: 1) The differential equation is equivalent to an integral equation if the function is continuous. 2) The operator maps continuous functions to continuous functions. 3) There exists a restriction of the domain where the operator maps within the range.
- Author
- Kamal Gour
- Language
- EN