On the Construction of a Variational Principle for a Certain Class of Differential-Difference Operator Equations
- Authors: Kolesnikova I.A.1
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Affiliations:
- Peoples’ Friendship University of Russia (RUDN University)
- Issue: Vol 67, No 2 (2021): Dedicated to the memory of Professor N. D. Kopachevsky
- Pages: 316-323
- Section: Articles
- URL: https://journals.rcsi.science/2413-3639/article/view/327666
- DOI: https://doi.org/10.22363/2413-3639-2021-67-2-316-323
- ID: 327666
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Abstract
In this paper, we obtain necessary and sufficient conditions for the existence of variational principles for a given first-order differential-difference operator equation with a special form of the linear operator Pλ(t) depending on t and the nonlinear operator Q. Under the corresponding conditions the functional is constructed. These conditions are obtained thanks to the well-known criterion of potentiality. Examples show how the inverse problem of the calculus of variations is constructed for given differentialdifference operators.
About the authors
I. A. Kolesnikova
Peoples’ Friendship University of Russia (RUDN University)
Author for correspondence.
Email: kolesnikova-ia@rudn.ru
Moscow, Russia
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