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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…