Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay

Abstract

We obtain a nonsmooth extension of Noether's symmetry theorem for variational problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed Euler-Lagrange extremals are restricted to those that satisfy the DuBois-Reymond necessary optimality condition. The important case of delayed variational problems with higher-order derivatives is considered as well.

This is a preprint of a paper whose final and definite form will be published in Applicable Analysis. Manuscript submitted 07-Nov-2012; accepted for publication 19-Dec-2012

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Cited by in corpus (5)

• Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem
• On a Non-Newtonian Calculus of Variations
• Optimal control with time-delays via the penalty method
• Lagrangian formalism and Noether-type theorems for second-order delay ODEs
• A survey on sufficient optimality conditions for delayed optimal control problems