Xia Huang

activity

20152026

R^{2 m}

with constant

Q

-curvature and arbitrary volume

11 citations · 30 across the 16 of their papers we have counts for

collaborators

17 papers

math.AP2026

Qualitative analysis of positive radial singular solutions on hyperbolic space

Xia Huang, Yahui Jiang, Chunyi Zhao

We investigate positive radial solutions with an isolated nonremovable singularity for the semilinear elliptic equation \begin{align*} Δ_{\mathbb{H}^N} u+λu+u^p=0 \qquad\text{in }\…

math.AP2026

Asymptotically sharp Hardy-Rellich inequalities on lattices

Xia Huang, Dong Ye

We determine the sharp asymptotic behavior of the optimal constants in the discrete Hardy-Rellich inequalities on the lattice $Z^{d}$ . For every fixed integer $m \geq 1$ , let…

math.AP2025

On Sharp Heisenberg Uncertainty Principle and the stability

Xia Huang, Dong Ye

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem.…

math.AP2025

Quantization of blow-up masses for the Finsler $N$ -Liouville equation

Xia Huang, Yuan Li, Dong Ye +1

The quantization results for blow-up phenomena play crucial roles in the analysis of partial differential equations. Here we quantify the blow-up masses to the following Finsler $N…

math.AP2025

Normal conformal metrics with prescribed $Q$ -Curvature in $R^{2 n}$

Xia Huang, Dong Ye, Feng Zhou

We consider the $Q$ -curvature equation \begin{equation}\label{0.1} (-Δ)^n u = K(x)e^{2nu}\quad\text{in} ~\mathbb{R}^{2n} \ (n \geq 2) \end{equation} where $K$ is a given non consta…

math.AP2024

On sharp anisotropic Hardy inequalities

Xia Huang, Dong Ye

Recently, Yanyan Li and Xukai Yan showed the following interesting Hardy inequalities with anisotropic weights: Let $n \geq 2$ , $p \geq 1$ , $p α > 1 - n$ , $p (α + β) > - n$ , then there exis…

math.AP2024

Higher order Hardy-Rellich identities

Xia Huang, Dong Ye

In this paper, we show Hardy-Rellich identities for polyharmonic operators $Δ^{m}$ and radial Laplacian $Δ_{r}^{m}$ in $R^{n}$ with Hardy-Hénon weight $∣ x ∣^{α}$ for all $m, n\in \ma…

math.AP2024

Symmetry of positive solutions to biharmonic Lane-Emden equation with singular set

Xia Huang, Yuan Li, Xianmei Zhou

In this paper, we are devoted to studying the positive weak, punctured or distributional solutions to the biharmonic Lane-Emden equation \begin{equation*} Δ^{2} u=u^{p} \quad \quad…

math.AP2022★ 6 cited

One dimensional sharp discrete Hardy-Rellich inequalities

Xia Huang, Dong Ye

In this paper, we establish discrete Hardy-Rellich inequalities on $N$ with $Δ^{\frac{ℓ}{2}}$ and optimal constants, for any $ℓ \geq 1$ . As far as we are aware, these…

math.AP2022

Super polyharmonic property and asymptotic behavior of solutions to the higher order Hardy-Hénon equation near isolated singularities

Xia Huang, Yuan Li, Hui Yang

In this paper, we are devoted to studying the positive solutions of the following higher order Hardy-Hénon equation $$ (-Δ)^{m}u=|x|^αu^{p} \quad\mbox{in}~ B_{1}\setminus\{0\}\subs…

math.AP2021★ 1 cited

First order Hardy inequalities revisited

Xia Huang, Dong Ye

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with…

math.AP2020★ 1 cited

Qualitative properties of Hénon type equations with exponential nonlinearity

Zongming Guo, Xia Huang, Dong Ye +1

We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of $Δu +…

math.AP2018★ 10 cited

Existence and nonexistence results for a weighted elliptic equation in exterior domains

Zongming Guo, Xia Huang, Dong Ye

We consider positive solution to the weighted elliptic problem \begin{equation*} \left \{ \begin{array}{ll} -{\rm div} (|x|^θ\nabla u)=|x|^\ell u^p \;\;\; \mbox{in $\mathbb{R}^N \b…

math.AP2018

Fast decaying solutions of Lane-Emden equations involving nonhomogeneous potential

Huyuan Chen, Xia Huang, Feng Zhou

We are interested in studying positive solutions of Lane-Emden equation $- Δ u = V u^{p} in R^{N} ∖ {0},$ where $V$ is a nonhomogeneous potential sati…

math.AP2017

On Delaunay solutions of a biharmonic elliptic equation with critical exponent

Zongming Guo, Xia Huang, Liping Wang +1

We are interested in the qualitative properties of positive entire solutions $u \in C^{4} (R^{n} \ {0})$ of the equation \begin{equation} \label{0.0} Δ^2 u=u^{\frac…

math.AP2015★ 1 cited

Existence of stable solutions to $(- Δ)^{m} u = e^{u}$ in $R^{N}$ with $m \geq 3$ and $N > 2 m$

Xia Huang, Dong Ye

We consider the polyharmonic equation $(- Δ)^{m} u = e^{u}$ in $R^{N}$ with $m \geq 3$ and $N > 2 m$ . We prove the existence of many entire stable solutions. This answer some questi…

math.AP2015★ 11 cited

Conformal metrics in $R^{2 m}$ with constant $Q$ -curvature and arbitrary volume

Xia Huang, Dong Ye

We study the polyharmonic problem $Δ^{m} u = \pm e^{u}$ in $R^{2 m}$ , with $m \geq 2$ . In particular, we prove that {\sl for any} $V > 0$ , there exist radial solutions of $Δ^m…

Qualitative analysis of positive radial singular solutions on hyperbolic space

Asymptotically sharp Hardy-Rellich inequalities on lattices

On Sharp Heisenberg Uncertainty Principle and the stability

Quantization of blow-up masses for the Finsler N-Liouville equation

Normal conformal metrics with prescribed Q-Curvature in R2n

On sharp anisotropic Hardy inequalities

Higher order Hardy-Rellich identities

Symmetry of positive solutions to biharmonic Lane-Emden equation with singular set

One dimensional sharp discrete Hardy-Rellich inequalities

Super polyharmonic property and asymptotic behavior of solutions to the higher order Hardy-Hénon equation near isolated singularities

First order Hardy inequalities revisited

Qualitative properties of Hénon type equations with exponential nonlinearity

Existence and nonexistence results for a weighted elliptic equation in exterior domains

Fast decaying solutions of Lane-Emden equations involving nonhomogeneous potential

On Delaunay solutions of a biharmonic elliptic equation with critical exponent

Existence of stable solutions to (−Δ)mu=eu in RN with m≥3 and N>2m

Conformal metrics in R2m with constant Q-curvature and arbitrary volume

Quantization of blow-up masses for the Finsler $N$ -Liouville equation

Normal conformal metrics with prescribed $Q$ -Curvature in $R^{2 n}$

Existence of stable solutions to $(- Δ)^{m} u = e^{u}$ in $R^{N}$ with $m \geq 3$ and $N > 2 m$

Conformal metrics in $R^{2 m}$ with constant $Q$ -curvature and arbitrary volume