{"ID":2824963,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21918","arxiv_id":"2512.21918","title":"On sufficient conditions in the classical problem of the calculus of variations","abstract":"This article is devoted to obtain new sufficient conditions for an extremum in problems of classical calculus of variations. The concept of a set of integrands is introduced. Using this concept, first and second order sufficient conditions for a weak and strong local minimum, as well as an absolute minimum were obtained. Also, this concept, in particular, allows us to define a class of variation problems for which the necessary Weierstrass condition is also sufficient condition. It is shown that the sufficient conditions for a minimum obtained here have new areas of application compared to the known sufficient conditions of the classical calculus of variations. The effectiveness of the obtained results is illustrated by examples.","short_abstract":"This article is devoted to obtain new sufficient conditions for an extremum in problems of classical calculus of variations. The concept of a set of integrands is introduced. Using this concept, first and second order sufficient conditions for a weak and strong local minimum, as well as an absolute minimum were obtaine...","url_abs":"https://arxiv.org/abs/2512.21918","url_pdf":"https://arxiv.org/pdf/2512.21918v1","authors":"[\"Misir J. Mardanov\",\"Telman K. Melikov\",\"Samin T. Malik\"]","published":"2025-12-26T08:25:53Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}