| Title:
|
On a class of $(p,q)$-Laplacian problems involving the critical Sobolev-Hardy exponents in starshaped domain (English) |
| Author:
|
Shahrokhi-Dehkordi, M.S. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
25 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
13-20 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Omega \subset \mathbb{R}^n$ be a bounded starshaped domain and consider the $(p,q)$-Laplacian problem \begin{align*} -\Delta_p u-\Delta_q u = \lambda ({\bf x} )\lvert u\rvert^{p^\star -2} u+\mu |u|^{r-2} u \end{align*} where $\mu$ is a positive parameter, $1 < q \le p < n$, $r\ge p^{\star}$ and $p^{\star}:=\frac{np}{n-p}$ is the critical Sobolev exponent. In this short note we address the question of non-existence for non-trivial solutions to the $(p, q)$-Laplacian problem. In particular we show the non-existence of non-trivial solutions to the problem by using a method based on Pohozaev identity. (English) |
| Keyword:
|
Quasi-linear elliptic problem |
| Keyword:
|
$(p,q)$-Laplacian operator |
| Keyword:
|
Critical Sobolev-Hardy exponent |
| Keyword:
|
Starshaped domain. |
| MSC:
|
35B33 |
| MSC:
|
35J20 |
| MSC:
|
35J92 |
| MSC:
|
58E05 |
| idZBL:
|
Zbl 1391.35170 |
| idMR:
|
MR3667073 |
| . |
| Date available:
|
2017-09-01T12:12:17Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146841 |
| . |
| Reference:
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