Blowing-up solutions to a critical 4D Neumann system in a competitive regime
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910088294301696 |
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| author | Guo, Qing Pistoia, Angela Wen, Shixin |
| author_facet | Guo, Qing Pistoia, Angela Wen, Shixin |
| contents | We build blowing-up solutions to the critical elliptic system with Neumann boundary condition,
\begin{equation*}
\begin{cases}
-Δu_1 + λu_1 = u_1^{3} -βu_1u_2^2 & \text{in } Ω,
-Δu_2 + λu_2 = u_2^{3} -βu_1^2u_2 & \text{in } Ω,
\frac{\partial u_1}{\partialν} = \frac{\partial u_2}{\partialν} = 0, & \text{on } \partial Ω,
\end{cases}
\end{equation*}
when $λ>0$ is sufficiently large in a competitive regime (i.e. $ β>0$) and in a domain $Ω\subset\mathbb R^4$ with smooth protrusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29329 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blowing-up solutions to a critical 4D Neumann system in a competitive regime Guo, Qing Pistoia, Angela Wen, Shixin Analysis of PDEs We build blowing-up solutions to the critical elliptic system with Neumann boundary condition, \begin{equation*} \begin{cases} -Δu_1 + λu_1 = u_1^{3} -βu_1u_2^2 & \text{in } Ω, -Δu_2 + λu_2 = u_2^{3} -βu_1^2u_2 & \text{in } Ω, \frac{\partial u_1}{\partialν} = \frac{\partial u_2}{\partialν} = 0, & \text{on } \partial Ω, \end{cases} \end{equation*} when $λ>0$ is sufficiently large in a competitive regime (i.e. $ β>0$) and in a domain $Ω\subset\mathbb R^4$ with smooth protrusions. |
| title | Blowing-up solutions to a critical 4D Neumann system in a competitive regime |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.29329 |