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MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 597-604 (2002)
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# 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 $$\Delta _p u+B(x,u)\leq 0,$$ 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 (MSC2000):** 35B05

**Full text of the article:**

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