Lagrangian formalism and Noether-type theorems for second-order delay ODEs

Abstract

The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for DODEs of second order are presented. Algebraic construction of integrals for DODEs based on symmetries are demonstrated by examples.

References in corpus (6)

• Continuous Symmetries of Difference Equations
• Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
• Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay
• Symmetries, conservation laws, invariant solutions and difference schemes of the one-dimensional Green-Naghdi equations
• Lie group classification of first-order delay ordinary differential equations
• Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries