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 ${\mathbb{W}}^{m,p}\left(\right[t_1,t_2];\mathbb{R})$ 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.

中文翻译：

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高阶变分和诺特定理中的组合泛函

在本文中，我们讨论了涉及泛函组合的高阶变分问题解的存在性和唯一性。此外，Sobolev 空间中的高阶 DuBois-Reymond 条件${\mathbb{W}}^{米,p}\left(\right[{吨}_1,{吨}_2];\mathbb{R})$被证明，无论是在积分形式和微分形式，并在额外的约束下。我们考虑高阶 Noether 定理并讨论主要问题的不变性条件。