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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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/
@article{CMFD_2021_67_2_a6,
author = {I. A. Kolesnikova},
title = {On the construction of a variational principle for a certain class of differential-difference operator equations},
journal = {Contemporary Mathematics. Fundamental Directions},
pages = {316--323},
year = {2021},
volume = {67},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_2_a6/}
}
TY - JOUR
AU - I. A. Kolesnikova
TI - On the construction of a variational principle for a certain class of differential-difference operator equations
JO - Contemporary Mathematics. Fundamental Directions
PY - 2021
SP - 316
EP - 323
VL - 67
IS - 2
UR - http://geodesic.mathdoc.fr/item/CMFD_2021_67_2_a6/
LA - ru
ID - CMFD_2021_67_2_a6
ER -
%0 Journal Article
%A I. A. Kolesnikova
%T On the construction of a variational principle for a certain class of differential-difference operator equations
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 316-323
%V 67
%N 2
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_2_a6/
%G ru
%F CMFD_2021_67_2_a6
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.
