Geodesic
On the Critical Exponents of Certain Nonlinear Boundary-Value Problems with Biharmonic Operator in the Exterior of a Ball
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 201-212 
Yu. V. Volodin. On the Critical Exponents of Certain Nonlinear Boundary-Value Problems with Biharmonic Operator in the Exterior of a Ball. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 201-212. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a4/
@article{MZM_2006_79_2_a4,
     author = {Yu. V. Volodin},
     title = {On the {Critical} {Exponents} of {Certain} {Nonlinear} {Boundary-Value} {Problems} with {Biharmonic} {Operator} in the {Exterior} of {a~Ball}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {201--212},
     year = {2006},
     volume = {79},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a4/}
}
TY  - JOUR
AU  - Yu. V. Volodin
TI  - On the Critical Exponents of Certain Nonlinear Boundary-Value Problems with Biharmonic Operator in the Exterior of a Ball
JO  - Matematičeskie zametki
PY  - 2006
SP  - 201
EP  - 212
VL  - 79
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a4/
LA  - ru
ID  - MZM_2006_79_2_a4
ER  - 
%0 Journal Article
%A Yu. V. Volodin
%T On the Critical Exponents of Certain Nonlinear Boundary-Value Problems with Biharmonic Operator in the Exterior of a Ball
%J Matematičeskie zametki
%D 2006
%P 201-212
%V 79
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a4/
%G ru
%F MZM_2006_79_2_a4

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

We establish sufficient conditions for the absence of global solutions of the differential inequality $\Delta^2u\geqslant|u|^q$ in the exterior of a ball. We consider various boundary conditions and show that the critical exponents depend on these conditions. The proofs are based on the test function method developed by Mitidieri and Pokhozhaev.

[1] Mitidieri E., Pokhozhaev S. I., Apriornye otsenki i otsutstvie reshenii nelineinykh differentsialnykh uravnenii i neravenstv v chastnykh proizvodnykh, Tr. MIAN, 234, Nauka, M., 2001 | MR

[2] Mitidieri E., Pokhozhaev S. I., “Otsutstvie polozhitelnykh reshenii dlya kvazilineinykh ellipticheskikh zadach v $\mathbb R^N$”, Tr. MIAN, 227, Nauka, M., 1999, 192–222 | MR | Zbl

[3] Mitidieri E., Pokhozhaev S. I., “Otsutstvie globalnykh polozhitelnykh reshenii kvazilineinykh ellipticheskikh neravenstv”, Dokl. RAN, 359:4 (1998), 456–460 | MR | Zbl