Radial symmetry of positive solutions to quasilinear Hardy-Sobolev doubly critical systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909894148358144 |
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| author | Baldelli, Laura Esposito, Francesco Lopez-Soriano, Rafael Sciunzi, Berardino |
| author_facet | Baldelli, Laura Esposito, Francesco Lopez-Soriano, Rafael Sciunzi, Berardino |
| contents | The aim of this paper is to prove radial symmetry results for positive weak solutions with finite energy to the following quasilinear doubly critical system \begin{equation} \begin{cases} -Δ_p u\,=γ\frac{u^{p-1}}{|x|^p} + u^{p^*-1}+ ναu^{α-1} v^β& \text{in}\quad \mathbb{R}^n \\ -Δ_p v\,=γ\frac{v^{p-1}}{|x|^p} + v^{p^*-1}+ νβu^αv^{β-1} & \text{in}\quad\mathbb{R}^n, \end{cases} \end{equation} where $1<p<n$, $γ\in [0, Λ_{n,p})$ with $Λ_{n,p} = \left[(n-p)/p\right]^p$, $α, β> 1$ such that $α+ β= p^*=np/(n-p)$ and $ν>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Radial symmetry of positive solutions to quasilinear Hardy-Sobolev doubly critical systems Baldelli, Laura Esposito, Francesco Lopez-Soriano, Rafael Sciunzi, Berardino Analysis of PDEs 35J61, 35B50, 35B06, 35J47, The aim of this paper is to prove radial symmetry results for positive weak solutions with finite energy to the following quasilinear doubly critical system \begin{equation} \begin{cases} -Δ_p u\,=γ\frac{u^{p-1}}{|x|^p} + u^{p^*-1}+ ναu^{α-1} v^β& \text{in}\quad \mathbb{R}^n \\ -Δ_p v\,=γ\frac{v^{p-1}}{|x|^p} + v^{p^*-1}+ νβu^αv^{β-1} & \text{in}\quad\mathbb{R}^n, \end{cases} \end{equation} where $1<p<n$, $γ\in [0, Λ_{n,p})$ with $Λ_{n,p} = \left[(n-p)/p\right]^p$, $α, β> 1$ such that $α+ β= p^*=np/(n-p)$ and $ν>0$. |
| title | Radial symmetry of positive solutions to quasilinear Hardy-Sobolev doubly critical systems |
| topic | Analysis of PDEs 35J61, 35B50, 35B06, 35J47, |
| url | https://arxiv.org/abs/2511.06071 |