On a critical Hamiltonian system with Neumann boundary conditions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917708919996416 |
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| author | Pistoia, Angela Schiera, Delia |
| author_facet | Pistoia, Angela Schiera, Delia |
| contents | We consider the Hamiltonian system with Neumann boundary conditions: \[ -Δu + μu=v^{q }, \quad -Δv+ μv=u^{p} \quad \text{ in $Ω$}, \qquad
u, v >0 \quad \text{ in $Ω$,} \qquad \partial_νu= \partial_νv=0 \quad \text{ on $\partial Ω$, } \] where $μ>0$ is a parameter and $Ω$ is a smooth bounded domain in $\mathbb R^N .$
When $(p, q)$ approaches from below the critical hyperbola $N/(p+1) + N/(q+1)=N-2$, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a critical Hamiltonian system with Neumann boundary conditions Pistoia, Angela Schiera, Delia Analysis of PDEs We consider the Hamiltonian system with Neumann boundary conditions: \[ -Δu + μu=v^{q }, \quad -Δv+ μv=u^{p} \quad \text{ in $Ω$}, \qquad u, v >0 \quad \text{ in $Ω$,} \qquad \partial_νu= \partial_νv=0 \quad \text{ on $\partial Ω$, } \] where $μ>0$ is a parameter and $Ω$ is a smooth bounded domain in $\mathbb R^N .$ When $(p, q)$ approaches from below the critical hyperbola $N/(p+1) + N/(q+1)=N-2$, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value. |
| title | On a critical Hamiltonian system with Neumann boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.00794 |