| Title:
|
Existence of solutions for some quasilinear $\vec {p}(x)$-elliptic problem with Hardy potential (English) |
| Author:
|
Azroul, Elhoussine |
| Author:
|
Bouziani, Mohammed |
| Author:
|
Hjiaj, Hassane |
| Author:
|
Youssfi, Ahmed |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
299-324 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the anisotropic quasilinear elliptic Dirichlet problem $$ \begin {cases} \displaystyle -\sum _{i=1}^{N} D^{i} a_{i}(x,u,\nabla u) + |u|^{s(x)-1}u= f +\lambda \frac {|u|^{p_{0}(x)-2}u}{|x|^{p_{0}(x)}}&\text {in}\ \Omega ,\\ u = 0 & \text {on}\ \partial \Omega , \end {cases} $$ where $\Omega $ is an open bounded subset of $\Bbb R^N$ containing the origin. We show the existence of entropy solution for this equation where the data $f$ is assumed to be in $L^{1}(\Omega )$ and $\lambda $ is a positive constant. (English) |
| Keyword:
|
anisotropic variable exponent Sobolev space |
| Keyword:
|
quasilinear elliptic equation |
| Keyword:
|
Hardy potential |
| Keyword:
|
entropy solution |
| Keyword:
|
$L^{1}$-data |
| MSC:
|
35J15 |
| MSC:
|
35J62 |
| idZBL:
|
Zbl 07088853 |
| idMR:
|
MR3985859 |
| DOI:
|
10.21136/MB.2018.0093-17 |
| . |
| Date available:
|
2019-07-24T11:12:35Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147776 |
| . |
| Reference:
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