New type of solutions for the critical Lane-Emden system
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913199408807936 |
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| author | Chen, Wenjing Huang, Xiaomeng |
| author_facet | Chen, Wenjing Huang, Xiaomeng |
| contents | In this paper, we consider the critical Lane-Emden system \begin{align*} \begin{cases} -Δu=K_1(y)v^p,\quad y\in \mathbb{R}^N,&\\ -Δv=K_2(y)u^q,\quad y\in \mathbb{R}^N,&\\ u,v>0, \end{cases} \end{align*} where $N\geq 5$, $p,q\in (1,\infty)$ with $\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}$, $K_1(y)$ and $K_2(y)$ are positive radial potentials. Under suitable conditions on $K_1(y)$ and $K_2(y)$, we construct a new family of solutions to this system, which are centred at points lying on the top and the bottom circles of a cylinder. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_09713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New type of solutions for the critical Lane-Emden system Chen, Wenjing Huang, Xiaomeng Analysis of PDEs In this paper, we consider the critical Lane-Emden system \begin{align*} \begin{cases} -Δu=K_1(y)v^p,\quad y\in \mathbb{R}^N,&\\ -Δv=K_2(y)u^q,\quad y\in \mathbb{R}^N,&\\ u,v>0, \end{cases} \end{align*} where $N\geq 5$, $p,q\in (1,\infty)$ with $\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}$, $K_1(y)$ and $K_2(y)$ are positive radial potentials. Under suitable conditions on $K_1(y)$ and $K_2(y)$, we construct a new family of solutions to this system, which are centred at points lying on the top and the bottom circles of a cylinder. |
| title | New type of solutions for the critical Lane-Emden system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.09713 |