The Multiplier Problem of the Calculus of Variations for Scalar Ordinary Differential Equations

2017/10/04 by Hardy Chan, Chan, Hardy
Engineering · Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #Material Science and Thermodynamics #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1710.01428

openalex publication_date 2017/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the inverse problem of the calculus of variations one is asked to find a Lagrangian and a multiplier so that a given differential equation, after multiplying with the multiplier, becomes the Euler--Lagrange equation for the Lagrangian. An answer to this problem for the case of a scalar ordinary differential equation of order 2n, n≥ 2, is proposed.

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