Abstract
In the present paper, we discuss the existence and uniqueness of solution for higher-order calculus of variations problems, involving composition of functionals. Also, higher-order DuBois-Reymond conditions in the Sobolev space are proven, both in integral and differential form, and under additional constraints. We consider the higher-order Noether's theorem and discuss invariance conditions for the main problem.
Acknowledgments
J. Vanterler acknowledges the financial support of a PNPD-CAPES (88882.305834/2018-01) scholarship of the Postgraduate Program in Applied Mathematics of IMECC-Unicamp and Gasto S. F. Frederico acknowledges the financial support by Fundao Cearence de Apoio ao Desenvolvimento Cientfico e Tecnolgico (FUNCAP)-BOLSA BPI (n BP4-00172-00054.02.00/20).
Disclosure statement
No potential conflict of interest was reported by the author(s).