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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…
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…