On inverse variational problem for system with one degree of freedom

O. E. Zubelevich

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We consider the inverse variational problem for a nonautonomous dynamical system with one degree of freedom and prove several nonlocal existence theorems.

Keywords: Douglas–Helmholtz problem, Helmholtz conditions, inverse problem of Lagrangian mechanics.

MSC: 70H03,70H25,70H05,35A10,37J06,35F05

Received: 20.06.2025
Revised: 14.09.2025

DOI: 10.4213/tmf11028

 English version: Theoretical and Mathematical Physics, 2025, 225:3, 2128–2133

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