Gastao S. F. Frederico, Delfim F. M. Torres
Published 2007-04-06Version 1
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.
Comments: Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 2007
Journal: Applicable Analysis, Volume 86, Issue 9, 2007, pp. 1117-1126.
Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition --- Application to fractional variational problems
On the Boundary Control of Systems of Conservation Laws
Partial observations and conservation laws: Grey-box modeling in biotechnology and optogenetics
![QR code for arXiv:0704.0949 [math.OC]](http://oss.arxitics.com/images/favicon.svg)