Quasilinear elliptic problems with singular nonlinearities in half-spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909684702642176 |
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| author | Le, Phuong |
| author_facet | Le, Phuong |
| contents | We study the monotonicity and one-dimensional symmetry of positive solutions to the problem $-Δ_p u = f(u)$ in $\mathbb{R}^N_+$ under zero Dirichlet boundary condition, where $p>1$ and $f:(0,+\infty)\to\mathbb{R}$ is a locally Lipschitz continuous function with a possible singularity at zero. Classification results for the case $f(u)=\frac{1}{u^γ}$ with $γ>0$ are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasilinear elliptic problems with singular nonlinearities in half-spaces Le, Phuong Analysis of PDEs 35J92, 35J75, 35B06, 35B53 We study the monotonicity and one-dimensional symmetry of positive solutions to the problem $-Δ_p u = f(u)$ in $\mathbb{R}^N_+$ under zero Dirichlet boundary condition, where $p>1$ and $f:(0,+\infty)\to\mathbb{R}$ is a locally Lipschitz continuous function with a possible singularity at zero. Classification results for the case $f(u)=\frac{1}{u^γ}$ with $γ>0$ are also provided. |
| title | Quasilinear elliptic problems with singular nonlinearities in half-spaces |
| topic | Analysis of PDEs 35J92, 35J75, 35B06, 35B53 |
| url | https://arxiv.org/abs/2409.19557 |