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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
On the potentiality of a class of operators relative to local bilinear forms
Svetlana A. Budochkina, Ekaterina S. Dekhanova Peoples' Friendship University of Russia, Moscow
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.
Образец цитирования:
Svetlana A. Budochkina, Ekaterina S. Dekhanova, “On the potentiality of a class of operators relative to local bilinear forms”, Ural Math. J., 7:1 (2021), 26–37
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj135 https://www.mathnet.ru/rus/umj/v7/i1/p26
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