Boundary layer profiles of positive solutions for logistic equations with sublinear nonlinearity on the boundary
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909730039922688 |
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| author | Umezu, Kenichiro |
| author_facet | Umezu, Kenichiro |
| contents | In this paper, we consider the logistic elliptic equation $-Δu = u- u^{p}$ in a smooth bounded domain $Ω\subset \mathbb{R}^{N}$, $N\geq2$, equipped with the sublinear Neumann boundary condition $\frac{\partial u}{\partial ν} = μu^{q}$ on $\partial Ω$, where $0<q<1<p$, and $μ\geq0$ is a parameter. With sub- and super-solutions and a comparison principle for the equation, we analyze the asymptotic profile of a unique positive solution for the equation as $μ\to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary layer profiles of positive solutions for logistic equations with sublinear nonlinearity on the boundary Umezu, Kenichiro Analysis of PDEs 35B09, 35B30, 35B40, 35B51, 35J25, 35J66 In this paper, we consider the logistic elliptic equation $-Δu = u- u^{p}$ in a smooth bounded domain $Ω\subset \mathbb{R}^{N}$, $N\geq2$, equipped with the sublinear Neumann boundary condition $\frac{\partial u}{\partial ν} = μu^{q}$ on $\partial Ω$, where $0<q<1<p$, and $μ\geq0$ is a parameter. With sub- and super-solutions and a comparison principle for the equation, we analyze the asymptotic profile of a unique positive solution for the equation as $μ\to \infty$. |
| title | Boundary layer profiles of positive solutions for logistic equations with sublinear nonlinearity on the boundary |
| topic | Analysis of PDEs 35B09, 35B30, 35B40, 35B51, 35J25, 35J66 |
| url | https://arxiv.org/abs/2506.19237 |