Remarks on the calculus of variations on time scales

Abstract

The calculus of variations is a classical subject which has gain throughout the last three hundred years a level of rigor and elegance that only time can give. In this note we show that, contrary to the classical field, available formulations and results on the recent calculus of variations on time scales are still at the heuristic level.

References in corpus (2)

• Higher-Order Calculus of Variations on Time Scales
• Necessary optimality conditions for the calculus of variations on time scales

Cited by in corpus (13)

• Noether's Theorem on Time Scales
• Calculus of Variations on Time Scales with Nabla Derivatives
• The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
• Leitmann's direct method for fractional optimization problems
• Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
• Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition
• Time scales: from Nabla calculus to Delta calculus and vice versa via duality
• Optimality conditions for the calculus of variations with higher-order delta derivatives
• Integral Inequalities and their Applications to the Calculus of Variations on Time Scales
• On a Non-Newtonian Calculus of Variations
• Isoperimetric Problems of the Calculus of Variations on Time Scales
• Necessary conditions for linear noncooperative N-player delta differential games on time scales
• Variational Optimal-Control Problems with Delayed Arguments on Time Scales