Existence and uniqueness theorem for ODE: an overview

2016/05/17 by Swarup Poria, Poria, Swarup, Aman Dhiman +1
Mathematics · #FOS: Mathematics #History and Overview (math.HO) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1605.05317

openalex publication_date 2016/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of existence and uniqueness of solutions became important due to the lack of general formula for solving nonlinear ordinary differential equations (ODEs). Compact form of existence and uniqueness theory appeared nearly 200 years after the development of the theory of differential equation. In the article, we shall discuss briefly the differences between linear and nonlinear first order ODE in context of existence and uniqueness of solutions. Special emphasis is given on the Lipschitz continuous functions in the discussion.

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