Geodesic
The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions
Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 733-748.

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We obtain a number of necessary and sufficient strong ellipticity conditions for a functional-differential equation containing, in its leading part, orthotropic contractions of the argument of the unknown function. We establish the unique solvability of the first boundary-value problem and the discreteness, semiboundedness, and sectorial structure of its spectrum.
Keywords: strong elliptic functional-differential equation, first boundary-value problem, orthotropic contraction, Gårding-type inequality, strong ellipticity condition, Plancherel's theorem, Riesz theorem, difference operator.
Mots-clés : Fourier transform 
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L. E. Rossovskii; A. L. Tasevich. The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions. Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 733-748. http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a7/

[1] M. I. Vishik, “O silno ellipticheskikh sistemakh differentsialnykh uravnenii”, Matem. sb., 29:3 (1951), 615–676 | MR | Zbl

[2] L. Gårding, “Dirichlet's problem for linear elliptic partial differential equations”, Math. Scand., 1 (1953), 55–72 | MR | Zbl

[3] A. Skubachevskii, “The first boundary value problem for strongly elliptic differential-difference equations”, J. Differential Equations, 63:3 (1986), 332–361 | DOI | MR | Zbl

[4] L. E. Rossovskii, “Koertsitivnost funktsionalno-differentsialnykh uravnenii”, Matem. zametki, 59:1 (1996), 103–113 | DOI | MR | Zbl

[5] L. E. Rossovskii, “Kraevye zadachi dlya ellipticheskikh funktsionalno-differentsialnykh uravnenii s rastyazheniem i szhatiem argumentov”, Tr. MMO, 62, 2001, 199–228 | MR | Zbl

[6] L. E. Rossovskii, “O spektralnoi ustoichivosti funktsionalno-differentsialnykh uravnenii”, Matem. zametki, 90:6 (2011), 885–901 | DOI | MR | Zbl

[7] L. E. Rossovskii, “K voprosu o koertsitivnosti funktsionalno-differentsialnykh uravnenii”, Trudy Shestoi Mezhdunarodnoi konferentsii po differentsialnym i funktsionalno-differentsialnym uravneniyam (Moskva, 14–21 avgusta, 2011). Chast 1, SMFN, 45, RUDN, M., 2012, 122–131 | MR

[8] T. Kato, J. B. McLeod, “The functional-differential equation $y'(x)=ay(\lambda x)+by(x)$”, Bull. Amer. Math. Soc., 77 (1971), 891–937 | DOI | MR | Zbl

[9] J. R. Ockendon, A. B. Tayler, “The dynamics of a current collection system for an electric locomotive”, Proc. R. Soc. London. Ser. A, 322 (1971), 447–468 | DOI

[10] V. A. Ambartsumyan, “K teorii fluktuatsii yarkosti v mlechnom puti”, Dokl. AN SSSR, 44 (1944), 223–226 | MR

[11] A. J. Hall, G. C. Wake, “A functional differential equation arising in the modelling of cell growth”, J. Austral. Math. Soc. Ser. B, 30:4 (1989), 424–435 | DOI | MR | Zbl

[12] K. Kuk, L. E. Rossovskii, A. L. Skubachevskii, “Kraevaya zadacha dlya funktsionalno-differentsialnogo uravneniya s lineino preobrazovannym argumentom”, Differents. uravneniya, 31:8 (1995), 1348–1352 | MR | Zbl

[13] D. A. Neverova, A. L. Skubachevskii, “O klassicheskikh i obobschennykh resheniyakh kraevykh zadach dlya differentsialno-raznostnykh uravnenii s peremennymi koeffitsientami”, Matem. zametki, 94:5 (2013), 702–719 | DOI | MR | Zbl

[14] A. M. Selitskii, “Prostranstvo nachalnykh dannykh 3-i kraevoi zadachi dlya parabolicheskogo differentsialno-raznostnogo uravneniya v odnomernom sluchae”, Matem. zametki, 92:4 (2012), 636–640 | DOI | Zbl

[15] A. M. Selitskii, “Prostranstvo nachalnykh dannykh 2-i kraevoi zadachi dlya parabolicheskogo differentsialno-raznostnogo uravneniya v lipshitsevykh oblastyakh”, Matem. zametki, 94:3 (2013), 477–480 | DOI | MR | Zbl