The Picard-Lindelof Theorem, also called the Cauchy-Lipschitz Theorem, gives conditions under which an ordinary differential equation with an initial value has a unique solution defined on some interval around the initial point, requiring that the equation's right-hand side be continuous and satisfy a Lipschitz condition. Named for Emile Picard and Ernst Lindelof, it is the standard existence-and-uniqueness result taught in every first course on differential equations.
Facts
StatementFor an ordinary differential equation with an initial value, if the right-hand side is continuous and Lipschitz continuous in the dependent variable near the initial point, a unique solution exists on some interval around that point. 2 Classification
Statement Form Picard-Lindelof Theorem
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Source Picard-Lindelof Theorem (Wikipedia)
Source Picard-Lindelof Theorem (Wikipedia)
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Source Picard-Lindelöf theorem (Wikipedia)
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1. Wikipedia: Picard-Lindelöf theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In mathematics, specifically the study of differential equations, the Picard-Lindelöf theorem gives a set of sufficient (but not necessary) conditions under which an initial value problem has a unique solution.
2. Picard-Lindelof Theorem (Wikipedia)
Wikimedia FoundationLead paragraph, first sentence
In mathematics, specifically the study of differential equations, the Picard-Lindelöf theorem gives a set of sufficient (but not necessary) conditions under which an initial value problem has a unique solution.
Principal Result Of: Émile Picard, Lead sentence of the article on the result
The theorem is named after Émile Picard, Ernst Lindelöf, Rudolf Lipschitz and Augustin-Louis Cauchy.
Principal Result Of: Ernst Leonard Lindelöf, Lead sentence of the article on the result
The theorem is named after Émile Picard, Ernst Lindelöf, Rudolf Lipschitz and Augustin-Louis Cauchy.
View the Source Picard-Lindelöf theorem (Wikipedia)
Proved By: Ernst Leonard Lindelöf, Lead paragraphQuote, Proved By: Ernst Leonard Lindelöf, Lead paragraph
In mathematics, specifically the study of differential equations, the Picard-Lindelöf theorem gives a set of sufficient (but not necessary) conditions under which an initial value problem has a unique solution.
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