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Yahui Jiang

Publications and source records attributed to Yahui Jiang.

5 recordsLinked to original sources
arXiv2026

Structure of radial solutions to a Hénon type equation with exponential nonlinearity on the hyperbolic space

In this paper, we study the separation and stability properties of radial solutions to a Hénon-type equation with exponential nonlinearity on the hyperbolic space. By transforming the radial hyperbolic equation into a weighted Euclidean equation and applying well-established separation results in Euclidean space, we classify the solution structures or establish sharp alternatives for radial solutions throughout the full range $n\ge2$ and $α>-2$. We also give an affirmative answer to the open question recently posed by Huang and Zhao.

math.AP↗
arXiv2026

Rigidity of positive rupture solutions to a biharmonic equation with critical negative exponent

We establish two rigidity theorems for positive rupture solutions of the conformally invariant equation $Δ^2 u=u^{-7}$ in $\mathbb R^3\setminus\{0\}$, which extend continuously to the origin with $u(0)=0$. First, we prove that if the associated conformal metric $g=u^{-4}|dx|^2$ has nonnegative scalar curvature, then every such solution is radially symmetric and has the sharp rupture profile $u(x)\sim(\frac{4}{3})^{\frac{1}{4}}|x|^{\frac{1}{2}}$ as $x\to 0$; in particular, the metric is complete at the origin. The principal novelty is a global rigidity theorem requiring neither curvature nor symmetry: the single global condition $u(x)=o(|x|)$ at infinity forces $u(x)\equiv(\frac{4}{3})^{\frac{1}{4}}|x|^{\frac{1}{2}}$. This result provides a sharp answer to the uniqueness question posed by McKenna and Reichel in a class with no a priori symmetry assumption. Finally, we construct complementary examples demonstrating the essential roles of the curvature and growth hypotheses.

math.AP↗
arXiv2026

Qualitative analysis of positive radial singular solutions on hyperbolic space

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 }\mathbb{H}^N\setminus\{Q\}, \end{align*} where $N\geq 3$, $p>1$, $λ\le \frac{(N-1)^2}{4}$, and $Q\in\mathbb{H}^N$ is a prescribed pole. Our purpose is to describe how the locally Euclidean singular behavior near ${\{Q}\}$ interacts with the genuinely hyperbolic dynamics at infinity, and how this interaction changes across the Serrin and Sobolev critical exponents. For $\frac{N}{N-2}\le p<\frac{N+2}{N-2}$, we construct a family of positive radial singular solutions selecting the fast exponential mode at infinity. At the pole, these solutions exhibit the logarithmically corrected fundamental-solution profile when $p=\frac{N}{N-2}$, and the standard power-law profile when $\frac{N}{N-2} \frac{N+2}{N-2}$ with $λ\le\frac{ N(N-2)}{4}$, we prove existence and uniqueness of the global positive radial singular solution, derive its two-term local asymptotic expansion near the pole, and establish a sharp trichotomy for its behavior at infinity.

math.AP↗
arXiv2023

Semiclassical states for coupled nonlinear Schrödinger equations with a critical frequency

In this paper, we are concerned with the coupled nonlinear Schrödinger system \begin{align*} \begin{cases} -\varepsilon^{2}Δu+a(x)u=μ_{1}u^{3}+βv^{2}u \ \ \ \ \mbox{in}\ \mathbb{R}^{N},\\ -\varepsilon^{2}Δv+b(x)v=μ_{2}v^{3}+βu^{2}v \ \ \ \ \ \mbox{in}\ \mathbb{R}^{N}, \end{cases} \end{align*} where $1\leq N\leq3$, $μ_{1},μ_{2},β>0$, $a(x)$ and $b(x)$ are nonnegative continuous potentials, and $\varepsilon>0$ is a small parameter. We show the existence of positive ground state solutions for the system above and also establish the concentration behaviour as $\varepsilon\rightarrow0$, when $a(x)$ and $b(x)$ achieve 0 with a homogeneous behaviour or vanish in some nonempty open set with smooth boundary.

math.AP↗