12 citations · 19 across the 26 of their papers we have counts for
5 papers · 2 filters
Sharp fractional Hardy--Maz'ya remainders on half-spaces: angular reduction and energy stability
Shengbing Deng, Dehong Yang
For , , , and , we study the sharp half-space remainder \[ [u]_{s,p,+}^p-\mathcal D_{d,s,p}\int_{\mathbb R^d_+}x_d^{-sp}|u|^p\,dx \geqΛ_{d,s,p,τ}\int_{\mat…
Liouville Theorems and Sharp Homogeneity Defects for Weighted Potential Systems
Shengbing Deng, Bo Zhang
In this paper, we consider \[ \begin{cases} u=K*(|x|^αa_0(x)v^p)&\quad\hbox{in }\mathbb R^n,\\ v=K*(|x|^βb_0(x)u^q)&\quad\hbox{in }\mathbb R^n, \end{cases} \] where , $0<ρ<n…
Morse index and spectral asymptotics of least-energy solutions to the Choquard equation in planar domains
Jiaoping Chen, Wenjing Chen, Shengbing Deng
We investigate the Morse index and spectral asymptotics of least-energy solutions to the planar Choquard equation \begin{equation*} \begin{cases} -Δu = \displaystyle\left(\int_Ω \f…
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…