Noether's theorem for non-smooth extremals of variational problems with time delay

被引：21

作者：

Frederico, Gastao S. F. ^{[1
,2
]}

Odzijewicz, Tatiana ^{[1
]}

Torres, Delfim F. M. ^{[1
]}

机构：

[1] Univ Aveiro, Dept Math, CIDMA Ctr Res & Dev Math & Applicat, P-3810193 Aveiro, Portugal

[2] Univ Cape Verde, Dept Sci & Technol, Praia, Santiago, Cape Verde

来源：

APPLICABLE ANALYSIS | 2014年 / 93卷 / 01期

关键词：

time delays; invariance; symmetries; constants of motion; conservation laws; DuBois-Reymond necessary optimality condition; Noether's theorem; 49K05; 49S05; CALCULUS;

D O I：

10.1080/00036811.2012.762090

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a non-smooth 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.

引用

页码：153 / 170

页数：18

共 20 条

[1]

[Anonymous], 1996, UNDERGRADUATE TEXTS

[2] Noether's theorem on time scales [J].