| Title:
|
A Weighted Eigenvalue Problems Driven by both $p(\cdot )$-Harmonic and $p(\cdot )$-Biharmonic Operators (English) |
| Author:
|
Laghzal, Mohamed |
| Author:
|
Khalil, Abdelouahed El |
| Author:
|
Touzani, Abdelfattah |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
443-455 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence of at least one non-decreasing sequence of positive eigenvalues for the problem driven by both $p(\cdot )$-Harmonic and $p(\cdot )$-biharmonic operators \begin {gather*} \Delta _{p(x)}^2 u-\Delta _{p(x)}u=\lambda w(x)|u|^{q(x)-2}u \quad \text {in } \Omega ,\\ u\in W^{2,p(\cdot )}(\Omega )\cap W_0^{1,p(\cdot )}(\Omega )\,, \end {gather*} is proved by applying a local minimization and the theory of the generalized Lebesgue-Sobolev spaces $L^{p(\cdot )}(\Omega )$ and $W^{m,p(\cdot )}(\Omega )$. (English) |
| Keyword:
|
Palais-Smale condition |
| Keyword:
|
Ljusternick-Schnirelmann |
| Keyword:
|
Variational methods |
| Keyword:
|
$p(\cdot )$-biharmonic operator |
| Keyword:
|
$p(\cdot )$-harmonic operator |
| Keyword:
|
Variable exponent. |
| MSC:
|
35J35 |
| MSC:
|
47J10 |
| MSC:
|
58E05 |
| idZBL:
|
Zbl 07484379 |
| idMR:
|
MR4355414 |
| . |
| Date available:
|
2022-01-10T10:06:49Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149328 |
| . |
| Reference:
|
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