Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition

Abstract

We introduce the notion of strong local minimizer for the problems of the calculus of variations on time scales. Simple examples show that on a time scale a weak minimum is not necessarily a strong minimum. A time scale form of the Weierstrass necessary optimality condition is proved, which enables to include and generalize in the same result both continuous-time and discrete-time conditions.

arXiv commentPaper accepted 12/May/2009 for publication in the Proceedings of the Estonian Academy of Sciences

References in corpus (4)

• Noether's Theorem on Time Scales
• Calculus of Variations on Time Scales with Nabla Derivatives
• Higher-Order Calculus of Variations on Time Scales
• Remarks on the calculus of variations on time scales

Cited by in corpus (17)

• Discrete-Time Fractional Variational Problems
• The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Higher-order Hahn's quantum variational calculus
• 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
• A General Backwards Calculus of Variations via Duality
• Differential, integral, and variational delta-embeddings of Lagrangian systems
• Existence of solutions for dynamic inclusions on time scales via duality
• The contingent epiderivative and the calculus of variations on time scales
• Fractional Calculus on Time Scales
• The Variational Calculus on Time Scales
• Delta-Nabla Optimal Control Problems
• Variational Optimal-Control Problems with Delayed Arguments on Time Scales
• Nondifferentiable variational principles in terms of a quantum operator
• Necessary optimality conditions for infinite horizon variational problems on time scales
• Time Scales and Mathematica