12 citations · 19 across the 26 of their papers we have counts for
10 papers · 1 filter
Multiple blowing-up solutions for a slightly critical Lane-Emden system with non-power nonlinearity
Shengbing Deng, Fang Yu
In this paper, we study the following Lane-Emden system with nearly critical non-power nonlinearity \begin{eqnarray*} \left\{ \arraycolsep=1.5pt \begin{array}{lll} -Δu =\frac{|v|^{…
Normalized solutions for p-Laplacian equations with potential
Shengbing Deng, Qiaoran Wu
In this paper, we consider the existence of normalized solutions for the following -Laplacian equation \begin{equation*} \left\{\begin{array}{ll} -Δ_{p}u-V(x)\lvert u\rvert^{p-2…
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…
Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application
Shengbing Deng, Xingliang Tian
This paper is devoted to radial solutions of the following weighted fourth-order equation \begin{equation*} \mathrm{div}(|x|^α\nabla(\mathrm{div}(|x|^α\nabla u)))=u^{2^{**}_α-1},\q…
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-…
Normalized solutions for -Laplacian equation with critical Sobolev exponent and mixed nonlinearities
Shengbing Deng, Qiaoran Wu
In this paper, we consider the existence and multiplicity of normalized solutions for the following -Laplacian critical equation \begin{align*} \left\{\begin{array}{ll} -Δ_{p}u=…
Sign changing bubble tower solutions to a slightly subcritical elliptic problem with non-power nonlinearity
Shengbing Deng, Fang Yu
We study the following elliptic problem involving slightly subcritical non-power nonlinearity $$\left\{\begin{array}{lll} -Δu =\frac{|u|^{2^*-2}u}{[\ln(e+|u|)]^ε}\ \ &{\rm in}\ Ω,…
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}|Δu…
Remainder terms of a nonlocal Sobolev inequality1
Shengbing Deng, Xingliang Tian, Minbo Yang +1
In this note we study a nonlocal version of the Sobolev inequality \begin{equation*} \int_{\mathbb{R}^N}|\nabla u|^2 dx \geq S_{HLS}\left(\int_{\mathbb{R}^N}\big(|x|^{-α} \ast u^{2…
Stability of Hardy-Sobolev inequality involving p-Laplace
Shengbing Deng, Xingliang Tian
This paper is devoted to considering the following Hardy-Sobolev inequality \[ \int_{\mathbb{R}^N}|\nabla u|^p \mathrm{d}x \geq \mathcal{S}_β\left(\int_{\mathbb{R}^N}\frac{|u|^{p^*…