Geodesic
On the existence of variational principles for differential–difference evolution equations
Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 25-39 
V. M. Filippov; V. M. Savchin; S. A. Budochkina. On the existence of variational principles for differential–difference evolution equations. Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 25-39. http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a2/
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     language = {ru},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of existence of variational principles for wide classes of generally nonlinear differential-difference equations with nonpotential operators is investigated.

[1] Filippov V.M., Savchin V.M., Shorokhov S.G., Variatsionnye printsipy dlya nepotentsialnykh operatorov, Itogi nauki i tekhniki. Sovr. probl. matematiki. Noveishie dostizheniya, 40, VINITI, M., 1992 | MR | Zbl

[2] Savchin V.M., “An operator approach to Birkhoff's equations”, Vestn. RUDN. Matematika, 2:2 (1995), 111–123 | Zbl

[3] Savchin V.M., Budochkina S.A., “O strukture variatsionnogo uravneniya evolyutsionnogo tipa so vtoroi proizvodnoi po $t$”, Dif. uravneniya, 39:1 (2003), 118–124 | MR | Zbl

[4] Savchin V.M., Budochkina S.A., “O suschestvovanii variatsionnogo printsipa dlya operatornogo uravneniya so vtoroi proizvodnoi po vremeni”, Mat. zametki, 80:1 (2006), 87–94 | DOI | MR | Zbl

[5] Budotchkina S.A., Savchin V.M., “On indirect variational formulations for operator equations”, J. Funct. Spaces Appl., 5:3 (2007), 231–242 | DOI | MR | Zbl

[6] Myshkis A.D., Elsgolts L.E., “Sostoyanie i problemy teorii differentsialnykh uravnenii s otklonyayuschimsya argumentom”, UMN, 22:2 (1967), 21–57 | MR | Zbl

[7] Skubachevskii A.L., Elliptic functional differential equations and applications, Birkhäuser, Basel, 1997 | MR | Zbl

[8] Filippov V.M., Savchin V.M., “On the inverse problem of the calculus of variations (IPCV) for functional partial differential equations”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy matematicheskogo obrazovaniya, Tez. dokl. 2-i Mezhdunar. konf., posv. 80-letiyu L.D. Kudryavtseva, Fizmatlit, M., 2003, 235–236

[9] Popov A.M., “Usloviya potentsialnosti differentsialno-raznostnykh uravnenii”, Dif. uravneniya, 34:3 (1998), 422–424 | MR | Zbl

[10] Kolesnikova I.A., Popov A.M., Savchin V.M., “On variational formulations for functional differential equations”, J. Funct. Spaces Appl., 5:1 (2007), 89–101 | DOI | MR | Zbl

[11] Kolesnikova I.A., Savchin V.M., “On the existence of variational principles for a class of the evolutionary differential–difference equations”, J. Funct. Spaces Appl., 2012, 780382 | MR | Zbl