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arXiv · 2411.06149

An elementary proof of the existence and uniqueness of solutions to an initial value problem

Luca Tanganelli Castrillón
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Abstract

In this note, we show a classical result on the local existence and uniqueness of a solution to an initial value problem subject to a Lipschitz condition. We use only elementary tools from mathematical analysis, without involving any integration. We proceed by showing that the Cauchy iterates converge on a dense subset of the interval and subsequently proving that the extension of this limit function to the whole interval is a solution to the Cauchy problem.

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Luca Tanganelli Castrillón. 2024-11-09. An elementary proof of the existence and uniqueness of solutions to an initial value problem. https://arxiv.org/abs/2411.06149

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