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On the Construction of a Variational Principle for a Certain Class of Differential-Difference Operator Equations

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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 differential-difference operators.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), Moscow, Russia

    I. A. Kolesnikova

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  1. I. A. Kolesnikova
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Correspondence to I. A. Kolesnikova.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.

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Kolesnikova, I.A. On the Construction of a Variational Principle for a Certain Class of Differential-Difference Operator Equations. J Math Sci 278, 108–114 (2024). https://doi.org/10.1007/s10958-024-06908-5

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