6 papers · 1 filter
Concentration, Local Uniqueness, and Morse Index of Multi-bubble Solutions for a Critical Exponential Biharmonic Choquard Equation
Wenjing Chen, Shengbing Deng
Let be a bounded domain of class , let , and let be positive. We study the Navier problem \[ Δ^2u=\varepsilon^{8-α}K(x)e^{u…
Complete Spectrum and Sharp Local Stability for the Critical Exponential Biharmonic Choquard Equation in \(\mathbb R^{4}\)
Wenjing Chen, Shengbing Deng
We study the conformally invariant exponential biharmonic Choquard equation in \(\mathbb R^{4}\). Our principal result is the complete spectral resolution of the linearized operato…
On the stability constant of Caffarelli-Kohn-Nirenberg inequality
Shengbing Deng, Xingliang Tian
By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than does not hold on the {\em Felli-…
Stability of Rellich-Sobolev type inequality involving Hardy term for bi-Laplacian
Shengbing Deng, Xingliang Tian
For and , we first show a non-degenerate result of the extremal functions for the following Rellich-Sobolev type inequality \begin{align*} \int_{\mathbb{R}^N}|Î…
A note on the Lp-Sobolev inequality
Shengbing Deng, Xingliang Tian
The usual Sobolev inequality in , asserts that for and ,…
Symmetry breaking of extremals for the high order Caffarelli-Kohn-Nirenberg type inequalities
Shengbing Deng, Xingliang Tian
In this paper we give the first result about the precise symmetry and symmetry breaking regions of extremal functions for weighted second-order inequalities. Firstly, based on the…