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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 1
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Articles

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

Gastão S.F. FredericoDepartment of Mathematics, CIDMA – Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193Aveiro, Portugal.;Department of Science and Technology, University of Cape Verde, Praia, Santiago, Cape Verde.
,
Tatiana OdzijewiczDepartment of Mathematics, CIDMA – Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193Aveiro, Portugal.
&
Delfim F.M. TorresDepartment of Mathematics, CIDMA – Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193Aveiro, Portugal.Correspondence[email protected]
Pages 153-170 | Received 07 Nov 2012, Accepted 19 Dec 2012, Published online: 29 Jan 2013

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Gastão S. F. Frederico, J. Vanterler da C. Sousa & Ricardo Almeida. (2022) Composition functionals in higher order calculus of variations and Noether's theorem. Applicable Analysis 101:17, pages 6321-6338.
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G. S. F. Frederico, M. J. Lazo, M. N. F. Barreto & J. Paiva. (2022) Constants of motion for isoperimetric variational problems with time delay. Applicable Analysis 101:7, pages 2707-2725.
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Agnieszka B. Malinowska & Tatiana Odzijewicz. (2020) Multiobjective variational problems with time delay. Applicable Analysis 99:7, pages 1260-1269.
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Agnieszka B. Malinowska & Tatiana Odzijewicz. (2017) Second Noether’s theorem with time delay. Applicable Analysis 96:8, pages 1358-1378.
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Articles from other publishers (16)

Li-Qin Huang & Yi Zhang. (2024) Herglotz-type vakonomic dynamics and Noether theory of nonholonomic systems with delayed arguments. Chaos, Solitons & Fractals 182, pages 114854.
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Xingyu Ji, Zhengwei Yang & Xianghua Zhai. (2024) Noether Symmetry of Multi-Time-Delay Non-Conservative Mechanical System and Its Conserved Quantity. Symmetry 16:4, pages 475.
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Gastão Frederico, Matheus Jatkoske Lazo, Maria Nilde Barreto & José Vanterler da Costa Sousa. (2023) Higher-Order Noether’s Theorem for Isoperimetric Variational Problems. Journal of Optimization Theory and Applications 199:2, pages 541-568.
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Güler Başak ÖZNUR, Güher Gülçehre ÖZBEY, Yelda AYGARKÜÇÜKEVCİLİOĞLU & Rabia AKTAŞ. (2023) Miscellaneous properties of Sturm-Liouville problems in multiplicative calculus. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72:4, pages 1141-1154.
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Gastão S.F. Frederico, Paolo Giordano, Alexandr A. Bryzgalov & Matheus J. Lazo. (2022) Calculus of variations and optimal control for generalized functions. Nonlinear Analysis 216, pages 112718.
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Nematollah Kadkhoda & Armin Hadjian. (2021) Group classification and constructing conservation laws for time-fractional Sawada–Kotera–Parker–Dye equation. Journal of Pseudo-Differential Operators and Applications 12:4.
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Delfim F. M. Torres. (2021) On a Non-Newtonian Calculus of Variations. Axioms 10:3, pages 171.
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Yi Zhang. (2020) Herglotz’s Variational Problem for Non-Conservative System with Delayed Arguments under Lagrangian Framework and Its Noether’s Theorem. Symmetry 12:5, pages 845.
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Ana P. Lemos-Paião, Cristiana J. Silva & Delfim F. M. Torres. 2020. Mathematical Modelling and Analysis of Infectious Diseases. Mathematical Modelling and Analysis of Infectious Diseases 323 342 .
Saeede Rashidi, S. Reza Hejazi & Elham Dastranj. (2018) Approximate symmetry analysis of nonlinear Rayleigh-wave equation. International Journal of Geometric Methods in Modern Physics 15:04, pages 1850055.
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Saeede Rashidi & S. Reza Hejazi. (2017) Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny–Lin equation. International Journal of Geometric Methods in Modern Physics 14:12, pages 1750170.
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Ping-Ping Cai, Jing-Li Fu & Yong-Xin Guo. (2017) Lie symmetries and conserved quantities of the constraint mechanical systems on time scales. Reports on Mathematical Physics 79:3, pages 279-298.
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Stanislav Yur'evich Lukashchuk. (2015) О построении законов сохранения для интегро-дифференциальных уравнений дробного порядкаConstructing conservation laws for fractional-order integro-differential equations. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 184:2, pages 179-199.
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S. Yu. Lukashchuk. (2015) Constructing conservation laws for fractional-order integro-differential equations. Theoretical and Mathematical Physics 184:2, pages 1049-1066.
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Simão P. S. Santos, Natália Martins & Delfim F. M. Torres. (2015) Variational problems of Herglotz type with time delay: DuBois--Reymond condition and Noether's first theorem. Discrete & Continuous Dynamical Systems - A 35:9, pages 4593-4610.
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Mohammed Benharrat & Delfim F. M. Torres. (2014) Optimal Control with Time Delays via the Penalty Method. Mathematical Problems in Engineering 2014, pages 1-9.
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