Quasilinear elliptic problems with singular nonlinearities in half-spaces

Phuong Le

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arXiv · 2409.19557

Quasilinear elliptic problems with singular nonlinearities in half-spaces

Phuong Le

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Abstract

We study the monotonicity and one-dimensional symmetry of positive solutions to the problem $-\Delta_p u = f(u)$ 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 $f(u)=\frac{1}{u^\gamma}$ with $\gamma>0$ are also provided.

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Phuong Le. 2024-09-29. Quasilinear elliptic problems with singular nonlinearities in half-spaces. https://arxiv.org/abs/2409.19557

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