Picard–Lindelöf theorem

Existence and uniqueness of solutions to initial value problems / From Wikipedia, the free encyclopedia

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In mathematics, specifically the study of differential equations, the Picard–Lindelöf theorem gives a set of conditions under which an initial value problem has a unique solution. It is also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem.

Fields

List of named differential equations

Types

By variable type
Ordinary Partial Differential-algebraic Integro-differential Fractional Linear Non-linear
Dependent and independent variables Autonomous Coupled / Decoupled Exact Homogeneous / Nonhomogeneous
Features
Order Operator Notation

The theorem is named after Émile Picard, Ernst Lindelöf, Rudolf Lipschitz and Augustin-Louis Cauchy.

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