Phuong Le

collaborators

8 papers

math.AP2026

Solutions stable outside a compact set for anisotropic quasilinear equations with negative exponent or exponential nonlinearity

Nhat Vy Huynh, Phuong Le

We study the equations $Δ_{p}^{H} u = u^{- q}$ , $u > 0$ , and $- Δ_{p}^{H} u = e^{u}$ in $R^{N}$ , where $Δ_{p}^{H} u = div (H (\nabla u)^{p - 1} \nabla H (\nabla u))$ is the Finsler $p$ -Lap…

math.AP2026

The critical boundary value for a nonlinear Schrödinger equation in a half-space: rigidity and dimensional transition

Phuong Le

Let $w_{0}$ be the positive homoclinic solution of $- w^{''} + w = w^{p}$ and set $c_{p} = w_{0} (0)$ . We study bounded positive solutions of \[ -Δv+v=v^p\quad\text{in }\mathbb R^N_+, \qquad v=c_p\qu…

math.AP2026

Sharp Liouville thresholds and endpoint rigidity for finite Morse index solutions of the $p$ -Laplace Lane--Emden equation

Phuong Le

We study $- Δ_{p} u = ∣ u ∣^{q - 1} u$ in $R^{N}$ with $N > p \geq 2$ , for solutions that are stable outside a compact set, with no assumption of sign, boundedness or symmetry. Damascel…

math.AP2026

Phase transition, sharp asymptotics and symmetry for critical quasilinear Hartree equations beyond $σ = 2 p$

Phuong Le

We establish the sharp asymptotic and symmetry theory for the critical quasilinear Hartree equation \[ -Δ_pu=\big(|x|^{-σ}*u^{p^*_σ}\big)u^{p^*_σ-1} \quad\text{in }\mathbb R^N, \qq…

math.AP2026

Critical anisotropic $p$ -Laplace equations without finite energy: classification and a Schoen-type Harnack inequality

Phuong Le

Let $N \geq 2$ and $1 < p < N$ . Let $H$ be a possibly non-reversible Minkowski norm on $R^{N}$ , with $H \in C^{2} (R^{N} ∖ {0})$ and $D^{2} (H^{2} /2)$ uniformly positive def…

math.AP2026

Spreading--vanishing dynamics and speed selection in a free-boundary competition model under a shifting climate

Phuoc Vinh Dinh, Phuong Le, Tien Dung Nguyen

We study a free boundary problem for a diffusive Lotka--Volterra competition system describing the invasion of a new species into the habitat of a native competitor, where habitat…

math.AP2026

A free boundary problem for spreading of an invasive species in the territory of a native competitor under shifting climate

Phuoc Vinh Dinh, Phuong Le, Tien Dung Nguyen

In this paper we consider a free boundary problem for the spreading of an invasive species in the habitat of a native competitor. We assume that the invasive species benefits from…

math.AP2026

Radial solutions of quasilinear Hardy--Emden--Fowler equations: exact decay rates, Delaunay solutions, and nonexistence

Phuong Le

Let $N > p > 1$ , $s > - p$ , $0 < μ < μ ˉ := (\frac{N - p}{p})^{p}$ and $q > p - 1$ . We determine the behaviour at infinity of \emph{every} positive solution of the quasilinear Hardy--Emden-…

Solutions stable outside a compact set for anisotropic quasilinear equations with negative exponent or exponential nonlinearity

The critical boundary value for a nonlinear Schrödinger equation in a half-space: rigidity and dimensional transition

Sharp Liouville thresholds and endpoint rigidity for finite Morse index solutions of the p-Laplace Lane--Emden equation

Phase transition, sharp asymptotics and symmetry for critical quasilinear Hartree equations beyond σ=2p

Critical anisotropic p-Laplace equations without finite energy: classification and a Schoen-type Harnack inequality

Spreading--vanishing dynamics and speed selection in a free-boundary competition model under a shifting climate

A free boundary problem for spreading of an invasive species in the territory of a native competitor under shifting climate

Radial solutions of quasilinear Hardy--Emden--Fowler equations: exact decay rates, Delaunay solutions, and nonexistence

Sharp Liouville thresholds and endpoint rigidity for finite Morse index solutions of the $p$ -Laplace Lane--Emden equation

Phase transition, sharp asymptotics and symmetry for critical quasilinear Hartree equations beyond $σ = 2 p$

Critical anisotropic $p$ -Laplace equations without finite energy: classification and a Schoen-type Harnack inequality