Noether's symmetry theorem for nabla problems of the calculus of variations

DOI10.1016/j.aml.2010.07.013zbMath1205.49033arXiv1007.5178OpenAlexW2065869359WikidataQ57651137 ScholiaQ57651137MaRDI QIDQ602828

Natália Martins, Delfim F. M. Torres

Publication date: 5 November 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.5178

zbMATH Keywords

dualitytime scalescalculus of variationsDuBois-Reymond conditiondelta and nabla calculusNoether's symmetry theorem

Mathematics Subject Classification ID

Duality theory (optimization) (49N15) Optimality conditions for problems involving relations other than differential equations (49K21)

Related Items (28)

Lie symmetry and invariants for a generalized Birkhoffian system on time scales ⋮ Noether theorem for Birkhoffian systems on time scales ⋮ Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense ⋮ Constants of motion for isoperimetric variational problems with time delay ⋮ Optimality conditions for the calculus of variations with higher-order delta derivatives ⋮ Local and global conserved quantities involving generalized operators ⋮ Noether-type conserved quantities on time scales for Birkhoffian systems with delayed arguments ⋮ Higher-order Noether's theorem for isoperimetric variational problems ⋮ Reduction of Chaplygin equations for nonholonomic systems on time scales by means of the cyclic integral and energy integral ⋮ A complex Noether approach for variational partial differential equations ⋮ Noether's theorems of variable mass systems on time scales ⋮ Generalizing the variational theory on time scales to include the delta indefinite integral ⋮ Unnamed Item ⋮ Noether’s-type theorems on time scales ⋮ Noether theory for Birkhoffian systems with nabla derivatives ⋮ Conserved quantities for Hamiltonian systems on time scales ⋮ Lie symmetries and conserved quantities of the constraint mechanical systems on time scales ⋮ Time-scale version of generalized Birkhoffian mechanics and its symmetries and conserved quantities of Noether type ⋮ Noether’s theorem for non-smooth extremals of variational problems with time delay ⋮ Generalized transversality conditions for the Hahn quantum variational calculus ⋮ Noether theorem for non-conservative systems with time delay on time scales ⋮ The existence of solutions for dynamic inclusions on time scales via duality ⋮ Two-dimensional systems that arise from the Noether classification of Lagrangians on the line ⋮ Mei symmetry and new conserved quantities of time-scale Birkhoff's equations ⋮ Mei symmetry and conservation laws for time-scale nonshifted Hamilton equations ⋮ The second Noether theorem on time scales ⋮ Nonshifted dynamics of constrained systems on time scales under Lagrange framework and its Noether's theorem ⋮ Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Calculus of variations on time scales with nabla derivatives
• The second Euler-Lagrange equation of variational calculus on time scales
• Necessary and sufficient conditions for local Pareto optimality on time scales
• An exploration of combined dynamic derivatives on time scales and their applications
• Diamond-\(\alpha \) Jensen's inequality on time scales
• A production-inventory model of HMMS on time scales
• A formulation of Noether's theorem for fractional problems of the calculus of variations
• Variational \(q\)-calculus.
• Hamiltonian systems on time scales
• Dynamic equations on time scales: A survey
• Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations
• An application of time scales to economics
• Noether's theorem on time scales
• On the Noether theorem for optimal control
• Inequalities on Time Scales: A Survey
• Isoperimetric Problems on Time Scales with Nabla Derivatives
• The delta-nabla calculus of variations
• Strong minimizers of the calculus of variations on time scales and the Weierstrass condition
• Some linear and nonlinear integral inequalities on time scales in two independent variables

This page was built for publication: Noether's symmetry theorem for nabla problems of the calculus of variations