Geodesic
The Behavior of Solutions of Semilinear Elliptic Equations of Second Order of the Form $Lu=e^u$ in the Infinite Cylinder
Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 408-420.

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We consider a semilinear elliptic equation of second order with variable coefficients of the form $Lu=e^u$ in the semi-infinite cylinder whose solution satisfies a homogeneous Neumann condition on the lateral surface of the cylinder.
Keywords: semilinear elliptic equation, Neumann boundary condition, Dirichlet integral, Poincaré inequality, Hölder's inequality. 
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A. V. Neklyudov. The Behavior of Solutions of Semilinear Elliptic Equations of Second Order of the Form $Lu=e^u$ in the Infinite Cylinder. Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 408-420. http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a8/

[1] V. A. Kondratev, O. A. Oleinik, “Ob asimptotike reshenii nelineinykh ellipticheskikh uravnenii”, Mezhdunarodnyi seminar “Differentsialnye uravneniya i smezhnye voprosy” (pyatnadtsataya sessiya sovmestnykh zasedanii seminara im. I. G. Petrovskogo i Moskovskogo matematicheskogo obschestva 19–22 yanvarya 1993 goda), UMN, 48:4 (1993), 184–185

[2] O. Oleinik, Some Asymptotic Problems in the Theory of Partial Differential Equations, Lezioni Lincee, Cambridge, Cambridge Univ. Press, 1996 | MR | Zbl

[3] A. I. Nasrullaev, “Ob asimptotike reshenii zadachi Neimana dlya uravneniya $\Delta u-e^u=0$ v polubeskonechnom tsilindre”, UMN, 50:3 (1995), 161–162 | MR | Zbl

[4] O. A. Oleinik, “Ob uravnenii $\Delta u+k(x)e^u=0$”, UMN, 33:2 (1978), 203–204 | MR | Zbl

[5] A. I. Nasrullaev, “Ob odnom klasse nelineinykh uravnenii v neogranichennykh oblastyakh”, Mezhdunarodnaya konferentsiya “Differentsialnye uravneniya i smezhnye voprosy”, posvyaschennaya 95-letiyu so dnya rozhdeniya I. G. Petrovskogo (sovmestnye zasedaniya seminara imeni I. G. Petrovskogo i Moskovskogo matematicheskogo obschestva; vosemnadtsataya sessiya, 25–29 aprelya 1996 goda), UMN, 51:5 (1996), 160–161

[6] O. A. Oleinik, G. A. Iosifyan, “O povedenii na beskonechnosti reshenii ellipticheskikh uravnenii vtorogo poryadka v oblastyakh s nekompaktnoi granitsei”, Matem. sb., 112:4 (1980), 588–610 | MR | Zbl

[7] A. V. Neklyudov, “O zadache Neimana dlya divergentnykh ellipticheskikh uravnenii vysokogo poryadka v neogranichennoi oblasti, blizkoi k tsilindru”, Tr. sem. im. I. G. Petrovskogo, 16 (1991), 191–217 | MR | Zbl

[8] E. M. Landis, A. I. Ibragimov, “Zadachi Neimana v neogranichennykh oblastyakh”, Dokl. RAN, 343:1 (1995), 17–18 | MR | Zbl

[9] S. S. Lakhturov, “Ob asimptotike reshenii vtoroi kraevoi zadachi v neogranichennykh oblastyakh”, UMN, 35:4 (1980), 195–196 | MR | Zbl