On the exact inverse problem of the calculus of variations

2014/08/24 by Chrastinova, Veronika, Tryhuk, Vaclav
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.5610

Abstract

The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of the first--order variational integrals related to the second--order Euler--Lagrange systems.

Related

• The Multiplier Problem of the Calculus of Variations for Scalar Ordinary Differential Equations
• The inverse problem of the calculus of variations for systems of second-order partial differential equations in the plane
• Inverse problem in the calculus of variations -- functional and antiexact forms
• On the inverse problem of calculus of variations
• On the local structure of the Euler-Lagrange mapping of the calculus of variations