Geodesic
On the absence of global solutions of the Gauss equation and solutions in external areas
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2014), pp. 55-60.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider conditions under which the Gauss equation has no solutions defined in the whole space or in areas external with respect to a ball. The absence of solutions in external areas is established in the case when the number of independent variables is more than two. In the two-dimensional case we obtain conditions ensuring the absence of global solutions of the second-order elliptic equation with variable coefficients in its linear part.
Mots-clés : Gauss equation, absence of global solutions, absence of solutions in exterior domains. 
@article{IVM_2014_1_a4,
     author = {A. V. Neklyudov},
     title = {On the absence of global solutions of the {Gauss} equation and solutions in external areas},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--60},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_1_a4/}
}
TY  - JOUR
AU  - A. V. Neklyudov
TI  - On the absence of global solutions of the Gauss equation and solutions in external areas
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 55
EP  - 60
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_1_a4/
LA  - ru
ID  - IVM_2014_1_a4
ER  - 
%0 Journal Article
%A A. V. Neklyudov
%T On the absence of global solutions of the Gauss equation and solutions in external areas
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 55-60
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_1_a4/
%G ru
%F IVM_2014_1_a4
A. V. Neklyudov. On the absence of global solutions of the Gauss equation and solutions in external areas. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2014), pp. 55-60. http://geodesic.mathdoc.fr/item/IVM_2014_1_a4/

[1] Vekua I. N., “O nekotorykh svoistvakh reshenii uravneniya Gaussa”, Tr. matem. in-ta im. V. A. Steklova, 64, 1961, 5–8 | MR | Zbl

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

[3] Kametaka I., Oleinik O. A., “Ob asimptoticheskikh svoistvakh i neobkhodimykh usloviyakh suschestvovaniya reshenii nelineinykh ellipticheskikh uravnenii vtorogo poryadka”, Matem. sb., 107(149):4 (1978), 572–600 | MR | Zbl

[4] Flavin J. N., Knops R. J., Payne L. E., “Asymptotic behavior of solutions to semi-linear elliptic equations on the half-cylinder”, Z. Angew. Math. Phys., 43:3 (1992), 405–421 | DOI | MR | Zbl

[5] Oleinik O. A., Some asymptotic problems of the theory of partial differential equations, Lezioni Lincee, Cambridge University Press, 1996 | MR

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

[7] Neklyudov A. V., “Povedenie reshenii polulineinogo ellipticheskogo uravneniya vtorogo poryadka vida $Lu=e^u$ v beskonechnom tsilindre”, Matem. zametki, 85:3 (2009), 408–420 | DOI | MR | Zbl