| Title:
|
On positive solutions of quasilinear elliptic systems (English) |
| Author:
|
Cheng, Yuanji |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
681-687 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems \[ \left\rbrace \begin{array}{ll}-\Delta _p u = f(x,u,v), &\quad \text{in} \ \Omega , -\Delta _p v = g(x,u,v), &\quad \text{in} \ \Omega , u = v = 0, &\quad \text{on} \ \partial \Omega , \end{array}\right.\] where $-\Delta _p$ is the $p$-Laplace operator, $p>1$ and $\Omega $ is a $C^{1,\alpha }$-domain in $\mathbb R^n$. We prove an analogue of [7, 16] for the eigenvalue problem with $f(x,u,v)=\lambda _1 v^{p-1}$, $ g(x,u,v)=\lambda _2u^{p-1}$ and obtain a non-existence result of positive solutions for the general systems. (English) |
| Keyword:
|
Eigenvalue problem |
| Keyword:
|
Degenerate elliptic operator |
| Keyword:
|
Nonlinear systems |
| Keyword:
|
Positive solutions. |
| MSC:
|
35B05 |
| MSC:
|
35J55 |
| MSC:
|
35J65 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 0899.35032 |
| idMR:
|
MR1479312 |
| . |
| Date available:
|
2009-09-24T10:09:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127386 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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