MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 597-604, 2002

Positive solutions of inequality with
$p$-Laplacian in exterior domains

Robert Marik

Robert Marik, Dept. of Mathematics, Mendel University, Zemedelska 3, 613 00 Brno, Czech Republic, e-mail: marik@mendelu.cz

Abstract: In the paper the differential inequality
\Delta_p u+B(x,u)\leq0,
where $\Delta_p u=\div(\Vert\nabla u\Vert^{p-2}\nabla u)$, $p>1$, $B(x,u)\in C(\R^n\times\R,\R)$ 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.

Keywords: $p$-Laplacian, oscillation criteria

Classification (MSC 2000): 35B05

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