| Title:
|
Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in $\Bbb R^n$ (English) |
| Author:
|
Kandilakis, Dimitrios A. |
| Author:
|
Lyberopoulos, Athanasios N. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
645-658 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that, under appropriate structure conditions, the quasilinear Dirichlet problem $$ \cases -\operatorname{div}(|\nabla u|^{p-2}\nabla u) =f(x,u), \quad & x\in\Omega, \ u=0, & x\in\partial\Omega, \endcases $$ where $\Omega $is a bounded domain in $\Bbb R^n$, $1<p<+\infty $, admits two positive solutions $u_{0}$, $u_{1}$ in $W_{0}^{1,p}(\Omega)$ such that $0<u_{0}\leq u_{1}$ in $\Omega $, while $u_{0}$ is a local minimizer of the associated Euler-Lagrange functional. (English) |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
positive solutions |
| Keyword:
|
sub- and supersolutions |
| Keyword:
|
local minimizers |
| Keyword:
|
Palais-Smale condition |
| MSC:
|
35J20 |
| MSC:
|
35J60 |
| MSC:
|
35J70 |
| MSC:
|
47J30 |
| idZBL:
|
Zbl 1105.35311 |
| idMR:
|
MR2062881 |
| . |
| Date available:
|
2009-01-08T19:31:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119419 |
| . |
| Reference:
|
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| . |
