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Title: Positive solutions of inequality with $p$-Laplacian in exterior domains (English)
Author: Mařík, Robert
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 127
Issue: 4
Year: 2002
Pages: 597-604
Summary lang: English
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Category: math
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Summary: In the paper the differential inequality \[\Delta _p u+B(x,u)\le 0,\] where $\Delta _p u=\div (\Vert \nabla u\Vert ^{p-2}\nabla u)$, $p>1$, $B(x,u)\in C(\mathbb{R}^{n}\times \mathbb{R},\mathbb{R})$ is studied. Sufficient conditions on the function $B(x,u)$ are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool. (English)
Keyword: $p$-Laplacian
Keyword: oscillation criteria
MSC: 35B05
MSC: 35J60
MSC: 35R45
idZBL: Zbl 1074.35505
idMR: MR1942645
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Date available: 2009-09-24T22:05:42Z
Last updated: 2012-06-18
Stable URL: http://hdl.handle.net/10338.dmlcz/133960
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Reference: [2] O. Došlý, R. Mařík: Nonexistence of the positive solutions of partial differential equations with $p$-Laplacian.Acta Math. Hungar. 90 (2001), 89–107. MR 1910321
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Reference: [4] R. Mařík: Hartman-Wintner type theorem for PDE with $p$-Laplacian.EJQTDE, Proc. 6th Coll. QTDE, 2000, No. 18, 1–7. MR 1798668
Reference: [5] R. Mařík: Oscillation criteria for PDE with $p$-Laplacian via the Riccati technique.J. Math. Anal. Appl. 248 (2000), 290–308. MR 1772598
Reference: [6] E. W. Noussair, C. A. Swanson: Oscillation of semilinear elliptic inequalities by Riccati equation.Can. J. Math. 22 (1980), 908–923.
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