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.

2010 Mathematics Subject Classifications:

• 49K05
• 49S05

Acknowledgements

This work was supported in part by CNPq, CAPES and FAPERGS, Brazilian funding agencies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by CNPq, CAPES and FAPERGS, Brazilian funding agencies.