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Название: On the Potentiality of a Class of Operators Relative to Local Bilinear Forms
Авторы: Budochkina, S. A.
Dekhanova, E. S.
Дата публикации: 2021
Издатель: N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences
Ural Federal University named after the first President of Russia B.N. Yeltsin
Библиографическое описание: Budochkina S. A. On the Potentiality of a Class of Operators Relative to Local Bilinear Forms / S. A. Budochkina, E. S. Dekhanova. — DOI 10.15826/umj.2021.1.003. — Text : electronic // Ural Mathematical Journal. — 2021. — Volume 7. — № 1. — P. 26-37.
Аннотация: The inverse problem of the calculus of variations (IPCV) is solved for a second-order ordinary differential equation with the use of a local bilinear form. We apply methods of analytical dynamics, nonlinear functional analysis, and modern methods for solving the IPCV. In the paper, we obtain necessary and sufficient conditions for a given operator to be potential relative to a local bilinear form, construct the corresponding functional, i.e., found a solution to the IPCV, and define the structure of the considered equation with the potential operator. As a consequence, similar results are obtained when using a nonlocal bilinear form. Theoretical results are illustrated with some examples.
Ключевые слова: INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS
LOCAL BILINEAR FORM
POTENTIAL OPERATOR
CONDITIONS OF POTENTIALITY
URI: http://elar.urfu.ru/handle/10995/108589
Условия доступа: Creative Commons Attribution License
Текст лицензии: https://creativecommons.org/licenses/by/4.0/
ISSN: 2414-3952
DOI: 10.15826/umj.2021.1.003
Сведения о поддержке: This paper was partially supported by the RUDN University Strategic Academic Leadership Program and by the Russian Foundation for Basic Research (project no. 19-08-00261a).
Источники: Ural Mathematical Journal. 2021. Volume 7. № 1
Располагается в коллекциях:Ural Mathematical Journal

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