Geodesic
On the construction of a variational principle for a certain class of differential-difference operator equations
Contemporary Mathematics. Fundamental Directions, Dedicated to the memory of Professor N. D. Kopachevsky, Tome 67 (2021) no. 2, pp. 316-323

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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 $P_\lambda(t)$ 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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     title = {On the construction of a variational principle for a certain class of differential-difference operator equations},
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I. A. Kolesnikova. On the construction of a variational principle for a certain class of differential-difference operator equations. Contemporary Mathematics. Fundamental Directions, Dedicated to the memory of Professor N. D. Kopachevsky, Tome 67 (2021) no. 2, pp. 316-323. http://geodesic.mathdoc.fr/item/CMFD_2021_67_2_a6/