Asymptotic Properties of Solutions of the Dirichlet Problem in the Half-Plane for Differential-Difference Elliptic Equations
Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 566-576.

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The Dirichlet problem in the half-plane for elliptic equations containing, in addition to differential operators, the shift operator with respect to the variable parallel to the boundary of the domain is considered. The behavior of the solution as the variable orthogonal to the boundary of the domain increases unboundedly is studied.
Keywords: differential-difference equation, qualitative properties.
Mots-clés : elliptic equation
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A. B. Muravnik. Asymptotic Properties of Solutions of the Dirichlet Problem in the Half-Plane for Differential-Difference Elliptic Equations. Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 566-576. http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a8/

[1] A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications, Birkhäuser, Basel, 1997 | MR | Zbl

[2] A. L. Skubachevskii, “Neklassicheskie kraevye zadachi. I”, SMFN, 26, RUDN, M., 2007, 3–132 | MR | Zbl

[3] A. L. Skubachevskii, “Neklassicheskie kraevye zadachi. II”, Uravneniya v chastnykh proizvodnykh, SMFN, 33, RUDN, M., 2009, 3–179 | MR

[4] P. L. Gurevich, “Ellipticheskie zadachi s nelokalnymi kraevymi usloviyami i polugruppy Fellera”, Uravneniya v chastnykh proizvodnykh, SMFN, 38, RUDN, M., 2010, 3–173 | MR | Zbl

[5] L. E. Rossovskii, “Ellipticheskie funktsionalno-differentsialnye uravneniya so szhatiem i rastyazheniem argumentov neizvestnoi funktsii”, Funktsionalno-differentsialnye uravneniya, SMFN, 54, RUDN, M., 2014, 3–138

[6] V. A. Kondratev, E. M. Landis, “Kachestvennaya teoriya lineinykh differentsialnykh uravnenii v chastnykh proizvodnykh vtorogo poryadka”, Differentsialnye uravneniya s chastnymi proizvodnymi – 3, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 32, VINITI, M., 1988, 99–215 | MR | Zbl

[7] D. Gilbarg, N. Trudinger, Ellipticheskie uravneniya vtorogo poryadka, Mir, M., 1989

[8] V. N. Denisov, A. B. Muravnik, “Ob asimptotike resheniya zadachi Dirikhle dlya ellipticheskogo uravneniya v poluprostranstve”, Nelineinyi analiz i nelineinye differentsialnye uravneniya, Fizmatlit, M., 2003, 397–417 | MR | Zbl

[9] V. N. Denisov A. B. Muravnik, “On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations”, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 88–93 | DOI | MR | Zbl

[10] A. B. Muravnik, “O zadache Dirikhle v poluploskosti dlya differentsialno-raznostnykh ellipticheskikh uravnenii”, Trudy Sedmoi Mezhdunarodnoi konferentsii po differentsialnym i funktsionalno-differentsialnym uravneniyam, Moskva, 22–29 avgusta, 2014, Chast 3, SMFN, 60, RUDN, M., 2016, 102–113

[11] I. M. Gelfand, G. E. Shilov, “Preobrazovaniya Fure bystro rastuschikh funktsii i voprosy edinstvennosti resheniya zadachi Koshi”, UMN, 8:6 (1953), 3–54 | Zbl

[12] A. B. Muravnik, “Ob asimptotike resheniya zadachi Koshi dlya nekotorykh differentsialno-raznostnykh parabolicheskikh uravnenii”, Differents. uravneniya, 41:4 (2005), 538–548 | Zbl

[13] A. B. Muravnik, “Ob asimptotike reshenii nekotorykh parabolicheskikh uravnenii s nelokalnymi starshimi chlenami”, Tr. sem. im. I. G. Petrovskogo, 25 (2006), 143–183 | Zbl

[14] A. B. Muravnik, “On the Cauchy problem for differential-difference parabolic equations with high-order nonlocal terms of general kind”, Discrete Contin. Dyn. Syst., 16:3 (2006), 541–561 | DOI | MR | Zbl

[15] A. B. Muravnik, “Funktsionalno-differentsialnye parabolicheskie uravneniya: integralnye predstavleniya i kachestvennye svoistva reshenii zadachi Koshi”, Uravneniya v chastnykh proizvodnykh, SMFN, 52, RUDN, M., 2014, 3–141

[16] V. N. Denisov, “Ob asimptotike reshenii ellipticheskikh uravnenii”, DAN, 329:6 (1993), 695–697 | Zbl