Quasilinear elliptic problems with singular nonlinearities in half-spaces

2024/09/29 by Le, Phuong · 1 citation
#35B06 #35B53 #35J75 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.19557

Abstract

We study the monotonicity and one-dimensional symmetry of positive solutions to the problem -Δ_p u = f(u) in ℝ^N₊ under zero Dirichlet boundary condition, where p>1 and f:(0,+∞)→ℝ is a locally Lipschitz continuous function with a possible singularity at zero. Classification results for the case f(u)=(1)/(u^γ) with γ>0 are also provided.

Cited by

• Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient

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