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

Abstract

We prove a Noether-type symmetry theorem and a DuBois-Reymond necessary optimality condition for nabla problems of the calculus of variations on time scales.

Submitted 20/Oct/2009; Revised 27/Jan/2010; Accepted 28/July/2010; for publication in Applied Mathematics Letters

References in corpus (10)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Noether's Theorem on Time Scales
• Calculus of Variations on Time Scales with Nabla Derivatives
• Higher-Order Calculus of Variations on Time Scales
• Diamond-$\alpha$ Jensen's Inequality on Time Scales
• Isoperimetric problems on time scales with nabla derivatives
• The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
• The diamond-alpha Riemann integral and mean value theorems on time scales
• Necessary and sufficient conditions for local Pareto optimality on time scales
• A unified approach to the calculus of variations on time scales

Cited by in corpus (6)

• Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
• Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem
• Generalizing the variational theory on time scales to include the delta indefinite integral
• Optimality conditions for the calculus of variations with higher-order delta derivatives
• Necessary optimality conditions for infinite horizon variational problems on time scales
• The second Noether theorem on time scale