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 Connections
Sources
1. Wikipedia: Picard-Lindelöf theorem
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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)
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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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