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Symmetries and solutions of a third order equation
Noether's theorem for higher-order variational problems of Herglotz type
1. | Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro |
2. | Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro |
3. | CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal |
References:
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References:
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Simão P. S. Santos, Natália Martins, Delfim F. M. Torres. Variational problems of Herglotz type with time delay: DuBois--Reymond condition and Noether's first theorem. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4593-4610. doi: 10.3934/dcds.2015.35.4593 |
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Agnieszka B. Malinowska, Delfim F. M. Torres. Euler-Lagrange equations for composition functionals in calculus of variations on time scales. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 577-593. doi: 10.3934/dcds.2011.29.577 |
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Clara Carlota, António Ornelas. The DuBois-Reymond differential inclusion for autonomous optimal control problems with pointwise-constrained derivatives. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 467-484. doi: 10.3934/dcds.2011.29.467 |
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Gastão S. F. Frederico, Delfim F. M. Torres. Noether's symmetry Theorem for variational and optimal control problems with time delay. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 619-630. doi: 10.3934/naco.2012.2.619 |
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Simão P. S. Santos, Natália Martins, Delfim F. M. Torres. Noether currents for higher-order variational problems of Herglotz type with time delay. Discrete and Continuous Dynamical Systems - S, 2018, 11 (1) : 91-102. doi: 10.3934/dcdss.2018006 |
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Jacky Cresson, Fernando Jiménez, Sina Ober-Blöbaum. Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations. Journal of Geometric Mechanics, 2022, 14 (1) : 57-89. doi: 10.3934/jgm.2021012 |
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Hans Josef Pesch. Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 161-173. doi: 10.3934/naco.2013.3.161 |
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Leonardo Colombo, David Martín de Diego. Higher-order variational problems on lie groups and optimal control applications. Journal of Geometric Mechanics, 2014, 6 (4) : 451-478. doi: 10.3934/jgm.2014.6.451 |
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Anthony Bloch, Leonardo Colombo, Fernando Jiménez. The variational discretization of the constrained higher-order Lagrange-Poincaré equations. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 309-344. doi: 10.3934/dcds.2019013 |
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Yuan Xu, Xin Jin, Saiwei Wang, Yang Tang. Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1495-1518. doi: 10.3934/dcdss.2020377 |
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Eduardo Martínez. Higher-order variational calculus on Lie algebroids. Journal of Geometric Mechanics, 2015, 7 (1) : 81-108. doi: 10.3934/jgm.2015.7.81 |
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Min Zhu. On the higher-order b-family equation and Euler equations on the circle. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 3013-3024. doi: 10.3934/dcds.2014.34.3013 |
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Giovanni Bonfanti, Arrigo Cellina. The validity of the Euler-Lagrange equation. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 511-517. doi: 10.3934/dcds.2010.28.511 |
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Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli. On the validity of the Euler-Lagrange system. Communications on Pure and Applied Analysis, 2015, 14 (1) : 51-62. doi: 10.3934/cpaa.2015.14.51 |
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Stefano Bianchini. On the Euler-Lagrange equation for a variational problem. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 449-480. doi: 10.3934/dcds.2007.17.449 |
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Michał Jóźwikowski, Mikołaj Rotkiewicz. Bundle-theoretic methods for higher-order variational calculus. Journal of Geometric Mechanics, 2014, 6 (1) : 99-120. doi: 10.3934/jgm.2014.6.99 |
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Colin J. Cotter, Michael John Priestley Cullen. Particle relabelling symmetries and Noether's theorem for vertical slice models. Journal of Geometric Mechanics, 2019, 11 (2) : 139-151. doi: 10.3934/jgm.2019007 |
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Bernard Dacorogna, Giovanni Pisante, Ana Margarida Ribeiro. On non quasiconvex problems of the calculus of variations. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 961-983. doi: 10.3934/dcds.2005.13.961 |
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Felix Sadyrbaev. Nonlinear boundary value problems of the calculus of variations. Conference Publications, 2003, 2003 (Special) : 760-770. doi: 10.3934/proc.2003.2003.760 |
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