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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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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/

[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