Geodesic
Positive solutions of inequality with $p$-Laplacian in exterior domains
Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 597-604

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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.
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.
DOI : 10.21136/MB.2002.133960
Classification : 35B05, 35J60, 35R45
Keywords: $p$-Laplacian; oscillation criteria 
Mařík, Robert. Positive solutions of inequality with $p$-Laplacian in exterior domains. Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 597-604. doi: 10.21136/MB.2002.133960
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