12 citations · 19 across the 26 of their papers we have counts for
27 papers
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…
Gradient stability of Caffarelli-Kohn-Nirenberg inequality involving weighted p-Laplace
Shengbing Deng, Xingliang Tian
The best constant and extremal functions are well known of the following Caffarelli-Kohn-Nirenberg inequality \[ \int_{\mathbb{R}^N}|\nabla u|^p\frac{\mathrm{d}x}{|x|^μ}\geq \mathc…
A note on the Lp-Sobolev inequality
Shengbing Deng, Xingliang Tian
The usual Sobolev inequality in , asserts that for and ,…
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^*…
Caffarelli-Kohn-Nirenberg-type inequalities related to weighted -Laplace equations
Shengbing Deng, Xingliang Tian
We use a suitable transform related to Sobolev inequality to investigate the sharp constants and optimizers for some Caffarelli-Kohn-Nirenberg-type inequalities which are related t…
Normalized solutions for a Choquard equation with exponential growth in
Shengbing Deng, Junwei Yu
In this paper, we study the existence of normalized solutions to the following nonlinear Choquard equation with exponential growth \begin{align*} \left\{ \begin{aligned} &-Δu+λu=(I…
Normalized solutions for Schrödinger systems in dimension two
Shengbing Deng, Junwei Yu
In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger systems with exponential growth \begin{align*} \left\{ \begin{aligned} &-Δu+λ_{…
Existence of solution for a class of fractional Hamiltonian-type elliptic systems with exponential critical growth in R
Shengbing Deng, Junwei Yu
In this paper, we study the following class of fractional Hamiltonian systems: \begin{eqnarray*} \begin{aligned}\displaystyle \left\{ \arraycolsep=1.5pt \begin{array}{ll} (-Δ)^{\fr…
On a class of singular Hamiltonian Choquard-type elliptic systems with critical exponential growth
Shengbing Deng, Junwei Yu
In this paper, we study the following Hamiltonian Choquard-type elliptic systems involving singular weights \begin{eqnarray*} \begin{aligned}\displaystyle \left\{ \arraycolsep=1.5p…
Some weighted fourth-order Hardy-Henon equations
Shengbing Deng, Xingliang Tian
By using a suitable transform related to Sobolev inequality, we investigate the sharp constants and optimizers in radial space for the following weighted Caffarelli-Kohn-Nirenberg-…
Boundary concentration of peak solutions for fractional Schrödinger-Poisson system
Shengbing Deng, Xingliang Tian
The goal of this paper is to study the existence of peak solutions for the following fractional Schrödinger-Poisson system: \begin{eqnarray*} \left\{ \arraycolsep=1.5pt \begin{arra…
On a nonhomogeneous Kirchhoff type elliptic system with the singular Trudinger-Moser growth
Shengbing Deng, Xingliang Tian
The aim of this paper is to study the multiplicity of solutions for the following Kirchhoff type elliptic systems \begin{eqnarray*} \left\{ \arraycolsep=1.5pt \begin{array}{ll} -m\…
Existence and multiplicity of solutions to a Kirchhoff type elliptic system with Trudinger-Moser growth
Shengbing Deng, Xingliang Tian
This paper deals with the existence and multiplicity of solutions for a class of Kirchhoff type elliptic system involving the Trudinger-Moser exponential growth nonlinearities. We…