Phuong Le

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math.AP2025

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

Phuong Le

We study positive solutions to the problem $- I^_{p} u + ϑ ∣\nabla u ∣^{q} = \frac{1}{u ^{3}} + f (u)$ in $R_{+}^{N}$ with the zero Dirichlet boundary condition, where $p > 1$ , $…

math.AP2025

Boundary estimates for singular elliptic problems involving a gradient term

Phuong Le

We study the behavior of weak solutions to the singular quasilinear elliptic problem $- I^_{p} u + ϑ ∣\nabla u ∣^{q} = \frac{1}{u ^{3}} + f (u)$ , in a bounded domain with the Dirich…

math.AP2025

Quasilinear elliptic problems with singular nonlinearities in half-spaces

Phuong Le

We study the monotonicity and one-dimensional symmetry of positive solutions to the problem $- I^_{p} u = f (u)$ in $R_{+}^{N}$ under zero Dirichlet boundary condition, where $p>1…

math.AP2024

Symmetry of bounded solutions to quasilinear elliptic equations in a half-space

Phuong Le

Let $u$ be a bounded positive solution to the problem $- I^_{p} u = f (u)$ in $R_{+}^{N}$ with zero Dirichlet boundary condition, where $p > 1$ and $f$ is a locally Lipschitz contin…

math.AP2024

Singular semilinear elliptic equations in half-spaces

Phuong Le

We prove the monotonicity of positive solutions to the problem $- I^ u = f (u)$ in $R_{+}^{N} := {(x^{'}, x_{N}) \in R^{N} ∣ x_{N} > 0}$ under zero Dirichlet boundary condition…

math.AP2024

On $p$ -Laplace equations with a critical Hardy-Sobolev exponent and a Hardy potential

Phuong Le

For $N \geq 2$ and $1 < p < N$ , we classify all positive $D^{1, p} (R^{N})$ -solutions to $p$ -Laplace equations with a critical Hardy-Sobolev exponent and a Hardy potential.

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

Boundary estimates for singular elliptic problems involving a gradient term

Quasilinear elliptic problems with singular nonlinearities in half-spaces

Symmetry of bounded solutions to quasilinear elliptic equations in a half-space

Singular semilinear elliptic equations in half-spaces

On p-Laplace equations with a critical Hardy-Sobolev exponent and a Hardy potential

On $p$ -Laplace equations with a critical Hardy-Sobolev exponent and a Hardy potential