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Nonexistence results of positive entire solutions for quasilinear elliptic inequalities

  Published:1997-06-01
 Printed: Jun 1997
  • Yūki Naito
  • Hiroyuki Usami
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Abstract

This paper treats the quasilinear elliptic inequality $$ \div (|Du|^{m-2}Du) \geq p(x)u^{\sigma}, \quad x \in \Rs^N, $$ where $N \geq 2$, $m > 1$, $ \sigma > m - 1$, and $p \colon \Rs^N \rightarrow (0, \infty)$ is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When $p$ has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results.
MSC Classifications: 35J70, 35B05 show english descriptions Degenerate elliptic equations
Oscillation, zeros of solutions, mean value theorems, etc.
35J70 - Degenerate elliptic equations
35B05 - Oscillation, zeros of solutions, mean value theorems, etc.
 

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