1 citations · 1 across the 10 of their papers we have counts for
12 papers
Sharp stability near sums of ground states for fractional Schrödinger equations
Hua Chen, Yun-Lu Fan, Xin Liao
We study quantitative stability for the fractional Schrödinger equation near finite sums of widely separated positive ground states. For every , $0<s<1…
Heat Flow under Semi-Flat Collapse with Conic Renormalization
Xin Yu Liao
Motivated by the SYZ picture for the collapsing of elliptic K3 surfaces, we study heat kernels under semi-flat collapse of Ricci-flat Kähler manifolds (X_t, g(t)) fibered by flat 2…
Quantitative Stability of Two Weakly Interacting Kinks in the Stationary phi^6 Model
Xin Liao
We study the stationary phi^6 model given by the equation -phi''(x) + 2 phi(x) - 8 phi(x)^3 + 6 phi(x)^5 = 0 for x in R, and establish sharp quantitative stability estimates for co…
From nonlinear Schrödinger equation to interacting particle system: 1 < p < 2
Xin Liao, Juntao Lv
We investigate the limiting behavior of solutions with infinitely many peaks to nonlinear Schrödinger equations [-epsilon^2 Delta u_epsilon + u_epsilon = u_epsilon^p, u_epsilon > 0…
Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li +1
We study the following perturbation from symmetry problem for the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm]…
Sharp Stability of Global Compactness on the Heisenberg Group
Hua Chen, Yun-lu Fan, Xin Liao
In this paper, we establish a sharp stability inequality on the Heisenberg group for functions that are close to the sum of m weakly interacting Jerison-Lee bubbles. As a consequen…
Sharp Stability of near a finite sums of ground states
Hua Chen, Yun Lu Fan, Xin Liao
We establish sharp quantitative stability estimates near finite sums of ground states. The results depend on the dimension and the order of nonlinearity.
Liouville Theorem for Lane Emden Equation of Baouendi Grushin operators
Xin Liao, Hua Chen
In this paper, we establish a Liouville theorem for solutions to the Lane Emden equation involving Baouendi Grushin operators. We focus on solutions that are stable outside a compa…
Liouville Theorem for Lane-Emden Equation on the Heisenberg Group
Hua Chen, Xin Liao
This paper establishes some Liouville type results for solutions to the Lane Emden equation on the entire Heisenberg group, both in the stable and stable outside a compact set scen…
Dirichlet problem for a class of nonlinear degenerate elliptic operators with critical growth and logarithmic perturbation
Hua Chen, Xin Liao, Ming Zhang
In this paper, we investigate the existence of weak solutions for a class of degenerate elliptic Dirichlet problems with critical nonlinearity and a logarithmic perturbation
Stability of the second non trivial eigenvalue of the Neumann Laplacian
Xin Liao
In this paper, building on the ideas of Brasco and Pratelli (Geom. Funct. Anal., 22 (2012), 107-135), we establish a stability estimate for Bucur and Henrot's inequality (Acta Math…
Multiplicity of solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li +1
In this paper, we study the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm] u=0\hfill & \mbox{on}~\partialΩ, \end…