The number of positive solutions for n$n$‐coupled elliptic systems

We study the number of positive solutions to the n$n$‐coupled elliptic system −Δui=μiui2∗−1+∑j=1,j≠inβijuipij−1ujqij,ui∈D1,2(RN),i=1,2,…,n,$$\begin{align*} -\Delta u_i&=\mu _iu_i^{2^*-1}+\sum _{j=1,\,j\ne i}^n\beta _{ij}u_i^{p_{ij}-1}u_j^{q_{ij}},\ u_i\in \mathcal {D}^{1,2}(\mathbb {R}^N),\\ &am...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2024-12, Vol.110 (6), p.n/a
Main Authors: Jing, Yongtao, Liu, Haidong, Liu, Yanyan, Liu, Zhaoli, Wei, Juncheng
Format: Article
Language:English
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Summary:We study the number of positive solutions to the n$n$‐coupled elliptic system −Δui=μiui2∗−1+∑j=1,j≠inβijuipij−1ujqij,ui∈D1,2(RN),i=1,2,…,n,$$\begin{align*} -\Delta u_i&=\mu _iu_i^{2^*-1}+\sum _{j=1,\,j\ne i}^n\beta _{ij}u_i^{p_{ij}-1}u_j^{q_{ij}},\ u_i\in \mathcal {D}^{1,2}(\mathbb {R}^N),\\ &\quad i=1,2,\ldots ,n, \end{align*}$$where N⩾3$N\geqslant 3$, n⩾2$n\geqslant 2$, μi>0$\mu _i>0$, βij>0$\beta _{ij}>0$, pij
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.70040