 |
|
Nonexistence results of positive entire solutions for quasilinear elliptic inequalities |
Canad. Math. Bull. 40(1997), 244-253
Published:1997-06-01
Printed: Jun 1997
Printed: Jun 1997
- Yūki Naito
- Hiroyuki Usami
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 - Degenerate elliptic equations 35B05 - Oscillation, zeros of solutions, mean value theorems, etc. |