Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball
We prove the uniqueness of positive radial solution to the $(p,q)$-Laplacian problem \begin{equation*} \left\{ \begin{aligned} -\Delta _{p}u-\Delta _{q}u={}&\lambda f(u)\quad \text{in }\Omega , \\ u={}&0\quad \text{on }\partial \Omega ,% \end{aligned}% \right. \end{equation*} where $p>...
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| Format: | Article |
| Language: | English |
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University of Szeged
2025-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11412 |
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| _version_ | 1849318353707991040 |
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| author | Dang Dinh Hai Xiao Wang |
| author_facet | Dang Dinh Hai Xiao Wang |
| author_sort | Dang Dinh Hai |
| collection | DOAJ |
| description | We prove the uniqueness of positive radial solution to the $(p,q)$-Laplacian problem
\begin{equation*}
\left\{
\begin{aligned}
-\Delta _{p}u-\Delta _{q}u={}&\lambda f(u)\quad \text{in }\Omega , \\
u={}&0\quad \text{on }\partial \Omega ,%
\end{aligned}%
\right.
\end{equation*}
where $p>q>1$, $\Delta_{r}u=\operatorname{div}(|\nabla u|^{r-2}\nabla u)$, $\Omega
=B(0,1)$ is the open unit ball in $\mathbb{R}^{N}$, $f:(0,\infty )\rightarrow
\mathbb{R\ }$ is $q$-sublinear at $\infty $ with possible semipositone structure at $0$, and $\lambda >0$ is a large parameter. |
| format | Article |
| id | doaj-art-7ff9b21303e143a2aadd1f8b7b860c64 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-7ff9b21303e143a2aadd1f8b7b860c642025-08-20T03:50:53ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752025-07-0120253411310.14232/ejqtde.2025.1.3411412Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ballDang Dinh Hai0https://orcid.org/0000-0002-9927-0793Xiao WangMississippi State University, Mississippi State, USAWe prove the uniqueness of positive radial solution to the $(p,q)$-Laplacian problem \begin{equation*} \left\{ \begin{aligned} -\Delta _{p}u-\Delta _{q}u={}&\lambda f(u)\quad \text{in }\Omega , \\ u={}&0\quad \text{on }\partial \Omega ,% \end{aligned}% \right. \end{equation*} where $p>q>1$, $\Delta_{r}u=\operatorname{div}(|\nabla u|^{r-2}\nabla u)$, $\Omega =B(0,1)$ is the open unit ball in $\mathbb{R}^{N}$, $f:(0,\infty )\rightarrow \mathbb{R\ }$ is $q$-sublinear at $\infty $ with possible semipositone structure at $0$, and $\lambda >0$ is a large parameter.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11412$(pq)$-laplacianpositive solutionsuniqueness |
| spellingShingle | Dang Dinh Hai Xiao Wang Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball Electronic Journal of Qualitative Theory of Differential Equations $(p q)$-laplacian positive solutions uniqueness |
| title | Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball |
| title_full | Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball |
| title_fullStr | Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball |
| title_full_unstemmed | Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball |
| title_short | Uniqueness of positive radial solutions for a class of $(p,q)$-Laplacian problems in a ball |
| title_sort | uniqueness of positive radial solutions for a class of p q laplacian problems in a ball |
| topic | $(p q)$-laplacian positive solutions uniqueness |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11412 |
| work_keys_str_mv | AT dangdinhhai uniquenessofpositiveradialsolutionsforaclassofpqlaplacianproblemsinaball AT xiaowang uniquenessofpositiveradialsolutionsforaclassofpqlaplacianproblemsinaball |