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:

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

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