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Yahui Jiang

Publications and source records attributed to Yahui Jiang.

7 recordsLinked to original sources
arXiv2026

Delaunay classification of positive singular solutions to the critical Lane--Emden system

We classify positive classical solutions of the Lane--Emden system \begin{align*} \begin{cases} -Δu=v^p & ~~\text{in }\mathbb{R}^n\setminus\{0\},\\ -Δv=u^q &~~ \text{in }\mathbb{R}^n\setminus\{0\}, \end{cases} \end{align*} with a nonremovable singularity at $0$ (i.e., $\lim_{x\to0}u(x)=\lim_{x\to0}v(x)=+\infty$), where $n\ge3$ and $p,q>0$ satisfy \[ \frac1{p+1}+\frac1{q+1}=\frac{n-2}{n}. \] Without additional growth or integrability assumptions, we establish radial symmetry about the origin, strict radial decrease, and global two-sided power bounds for both components. Furthermore, every such solution can be written as \[ u(x)=|x|^{-α}U(\log|x|),\qquad v(x)=|x|^{-β}V(\log|x|), \] where $α=\frac{n}{q+1}$, $β=\frac{n}{p+1}$, and $(U,V)$ is either the positive equilibrium $(A,B)=((\fracαβ)^{\fracα{2}}, (\fracαβ)^{\fracβ{2}})$ or a positive nonconstant periodic solution of the associated Emden--Fowler system. These periodic solutions form a Delaunay family: for every $\varepsilon\in(0,A)$, there is a unique profile pair, up to translation in $t=\log|x|$, with $\min_{\mathbb{R}}U=\varepsilon$. The Hamiltonian energy provides an alternative parameter, decreasing continuously and strictly from zero to the equilibrium energy as $\varepsilon$ increases from $0$ to $A$. The common least period of the two components tends to infinity as $\varepsilon\downarrow0$ and to the period of the linearized oscillation at $(A,B)$ as $\varepsilon\uparrow A$. The classification includes the case of a sublinear exponent.

math.AP↗
arXiv2026

EP251129a: A Fast X-ray Transient with Two X-Ray Plateaus and Its Off-axis Afterglow

Extragalactic fast X-ray transients (EFXTs) detected by the Einstein Probe are extending the parameter space of relativistic stellar explosions toward softer and longer-lived transients. Here we report EP251129a/GRB 251129A at z=0.505, which exhibits two X-ray plateaus: an early plateau lasting $\sim 10^{4}\,\rm s$ followed by a rapid decay with spectral softening, and a second plateau extending to 60 days, placing it at the extreme long-duration end of Gamma Ray Burst (GRB) plateaus. The early optical emission evolves independently of the X-ray, indicating a different origin; whereas the unusual radio afterglow shows a rapid rise of $F_ν\propto t^{1.9-2.5}$ and a delayed peak at $\sim36-40$ days, providing strong evidence for an off-axis geometry. We find that the early X-ray behavior resembles those of ultra-long GRBs (ULGRBs) and can be naturally explained by the internal dissipation from a newborn millisecond magnetar undergoing gravitational-wave-dominated spin-down before collapsing into a black hole. The early optical, radio and late X-ray emission are well described by an off-axis two-component jet afterglow with additional energy injection, possibly powered by fallback accretion onto black hole. EP251129a therefore connects the emerging EFXT population with ULGRB-like central-engine activity and off-axis afterglow, offering a rare opportunity to probe both the evolution of central engine and jet structure in a single event.

astro-ph.HE↗
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↗