The functional formulation of second-order ordinary differential equations

2003/10/28 by P. Chladek, Chladek, P.
Engineering · Mathematics · #34A12 #39B52 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #Numerical methods for differential equations #math.CA #math.DS #msc:34A12 #msc:39B52

paper · pdf · doi:10.48550/arxiv.math/0310443

8 pages, Latex

arxiv created 2003/10/28 · openalex publication_date 2003/10/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the necessary and sufficient conditions in order that a smooth mapping F be a dependence of a complete solution of some second-order ordinary differential equation on Neumann conditions are deduced. These necessary and sufficient conditions consist of functional equations for F and of a smooth extensibility condition. Illustrative examples are presented to demonstrate this result. In these examples, the mentioned functional equations for F are related to the functional equations for geodesics, to Jensen's equation, to the functional equations for conic sections and to Neuman's result for linear ordinary differential equations.

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