Composition functionals in higher order calculus of variations and Noether's theorem. Issue 17 (22nd November 2022) - Frederico, Gastão S. F.; Sousa, J. Vanterler da C.; Almeida, Ricardo
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 W m, p ( [ t 1, t 2 ] ; R ) 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.