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

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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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