ON THE POTENTIALITY OF A CLASS OF OPERATORS RELATIVE TO LOCAL BILINEAR FORMS
| Autor: | Ekaterina S. Dekhanova, S. A. Budochkina |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Class (set theory)
General Mathematics Structure (category theory) Bilinear form Inverse problem Analytical dynamics INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS Operator (computer programming) inverse problem of the calculus of variations local bilinear form potential operator conditions of potentiality CONDITIONS OF POTENTIALITY Ordinary differential equation LOCAL BILINEAR FORM QA1-939 Nonlinear functional analysis Applied mathematics POTENTIAL OPERATOR Mathematics |
| Zdroj: | Ural Mathematical Journal, Vol 7, Iss 1 (2021) |
| ISSN: | 2414-3952 |
| DOI: | 10.15826/umj.2021.1.003 |
| Popis: | 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. 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). |
| Databáze: | OpenAIRE |
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