Geodesic
Inverse Problem of the Calculus of Variations for Systems of Differential-Difference Equations of Second Order
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 745-749 Cet article a éte moissonné depuis la source Math-Net.Ru

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The inverse problem of the calculus of variations for second-order nonlinear and linear systems of differential-difference equations is considered. The relationship between the formal potentiality of a linear system with constant coefficients and the parity of its characteristic function is established. 
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A. M. Popov. Inverse Problem of the Calculus of Variations for Systems of Differential-Difference Equations of Second Order. Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 745-749. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a13/

[1] Filippov V. M., Savchin V. M., Shorokhov S. G., Variatsionnye printsipy dlya nepotentsialnykh operatorov, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie dostizheniya, 40, VINITI, M., 1992

[2] Gelmgolts G., “O fizicheskom znachenii printsipa naimenshego deistviya”, Variatsionnye printsipy mekhaniki, ed. L. S. Polak, M., 1959, 430–459

[3] Popov A. M., “Usloviya potentsialnosti Gelmgoltsa dlya sistem differentsialno-raznostnykh uravnenii”, Matem. zametki, 64:3 (1998), 437–442 | MR | Zbl

[4] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | Zbl