The Schwarzian derivative and Euler-Lagrange equations

被引：1

作者：

Krynski, Wojciech ^{[1
]}

机构：

[1] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2022年 / 182卷

关键词：

Schwarzian derivative; Euler-Lagrange equations; Geometry of ODEs;

D O I：

10.1016/j.geomphys.2022.104665

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Schwarzian derivative from a variational viewpoint. In particular, we show that the Schwarzian derivative defines a first integral of the Euler-Lagrange equation of a second order Lagrangian. Moreover, we prove that the Schwarzian derivative itself can be considered as the Euler-Lagrange operator for an appropriately chosen class of variations. (C) 2022 The Author(s). Published by Elsevier B.V.

引用

页数：7

共 50 条

[41] On the validity of the maximum principle and of the Euler-Lagrange equation for a minimum problem depending on the gradient
Cellina, A
Perrotta, S
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (06) : 1987 - 1998
[42] On the euler-lagrange equation for functionals of the calculus of variations without upper growth conditions
Degiovanni, Marco
Marzocchi, Marco
[J]. SIAM Journal on Control and Optimization, 2009, 48 (04) : 2857 - 2870
[43] Model-free control approach to uncertain Euler-Lagrange equations with a Lyapunov-based LOO-gain analysis
Park, Hae Yeon
Kim, Jung Hoon
[J]. AIMS MATHEMATICS, 2023, 8 (08): : 17666 - 17686
[44] Dichotomy results for delay differential equations with negative Schwarzian derivative
Liz, Eduardo
Roest, Gergely
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (03) : 1422 - 1430
[45] The Schwarzian derivative in ℝn
Tao Qian
Qihuang Yu
[J]. Advances in Applied Clifford Algebras, 2001, 11 (Suppl 2) : 257 - 268
[46] A new optimal control approach to uncertain Euler-Lagrange equations: H∞ disturbance estimator and generalized H2 tracking controller
Kim, Taewan
Kim, Jung Hoon
[J]. AIMS MATHEMATICS, 2024, 9 (12): : 34466 - 34487
[47] Extension of the Euler Lagrange equations to a wider class of nonlinear problems
Rouff, M
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 178 (3-4) : 263 - 265
[48] Euler—Lagrange Equations for Functionals Defined On Fréchet Manifolds
José Antonio Vallejo
[J]. Journal of Nonlinear Mathematical Physics, 2009, 16 : 443 - 454
[49] The Schwarzian derivative in Kahler manifolds
龚昇
余其煌
[J]. Science China Mathematics, 1995, (09) : 1033 - 1048
[50] Schwarzian derivative and convexity of order α
Malik, Somya
Ravichandran, V
[J]. JOURNAL OF ANALYSIS, 2023, 31 (01) : 201 - 228

← 1 2 3 4 5 →