Constants of motion for Isoperimetric Variational Problems with Time Delay

Abstract

In the present work, we obtain the constants of motion for isoperimetric variational problems with time delay. We consider a constrained optimization problem where the Lagrangian function defining the functional depends on time delayed arguments. We prove the isoperimetric Euler--Lagrange and DuBois--Reymond type optimality conditions and, in order to investigate the constants of motion for this problem, we obtain a nonsmooth extension of Noether's symmetry theorem for isoperimetric variational problems with delayed arguments.

accepted to publication in Applicable Analysis

References in corpus (4)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Noether's Theorem on Time Scales
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

Cited by in corpus (1)

• Hight-order Noether's Theorem for Nonsmooth Extremals of Isoperimetric Variational Problems with Time Delay