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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…
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.
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 >…
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…
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…