Abstract
We study a variable end-points calculus of variations problem of Bolza containing inequality and equality constraints. The proof of the principal theorem of the paper has a direct nature since it is independent of some classical sufficiency approaches invoking the Hamiltonian-Jacobi theory, Riccati equations, fields of extremals or the theory of conjugate points. In contrast, the algorithm employed to prove the principal theorem of the article is based on elementary tools of the real analysis.
Highlights
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We study a nonparametric calculus of variations problem of Bolza having variable end-points, isoperimetric inequality and equality restrictions and mixed inequality and equality pointwise restraints
The technique used in this article to obtain the main theorem of the paper corresponds to a generalization of a method originally introduced by Hestenes in [9]
Summary
Straightforward Sufficiency Proof for a Nonparametric Problem of Bolza in the Calculus of Variations. The technique used in this article to obtain the main theorem of the paper corresponds to a generalization of a method originally introduced by Hestenes in [9] This algorithm have been generalized in [19,20,21] for the case of a parametric problem of the calculus of variations, a direct sufficiency proof for the nonparametric problem of.
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