| Title:
|
Existence of infinitely many weak solutions for some quasilinear $\vec {p}(x)$-elliptic Neumann problems (English) |
| Author:
|
Ahmed, Ahmed |
| Author:
|
Ahmedatt, Taghi |
| Author:
|
Hjiaj, Hassane |
| Author:
|
Touzani, Abdelfattah |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
142 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
243-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the following quasilinear Neumann boundary-value problem of the type $$ \begin {cases} -\displaystyle \sum _{i=1}^{N}\frac {\partial }{\partial x_{i}}a_{i}\Big (x,\frac {\partial u}{\partial x_{i}}\Big ) + b(x)|u|^{p_{0}(x)-2}u = f(x,u)+ g(x,u) &\text {in} \ \Omega , \\ \quad \dfrac {\partial u}{\partial \gamma } = 0 &\text {on} \ \partial \Omega . \end {cases} $$ We prove the existence of infinitely many weak solutions for our equation in the anisotropic variable exponent Sobolev spaces and we give some examples. (English) |
| Keyword:
|
Neumann problem |
| Keyword:
|
quasilinear elliptic equation |
| Keyword:
|
weak solution |
| Keyword:
|
variational principle |
| Keyword:
|
anisotropic variable exponent Sobolev space |
| MSC:
|
35D30 |
| MSC:
|
35J20 |
| MSC:
|
35J25 |
| MSC:
|
35J62 |
| idZBL:
|
Zbl 06770144 |
| idMR:
|
MR3695465 |
| DOI:
|
10.21136/MB.2017.0037-15 |
| . |
| Date available:
|
2017-08-31T12:39:56Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146824 |
| . |
| Reference:
|
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| Reference:
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