4 papers
On the Stein-Weiss inequalities and higher-order Caffarelli-Kohn-Nirenberg type inequalities: sharp constants, symmetry of extremal functions
Shengbing Deng, Xingliang Tian
In this paper, we first classify all radially symmetry solutions of the following weighted fourth-order equation \begin{equation*} Δ(|x|^{-γ}Δu)=|x|^γu^{\frac{N+4+3γ}{N-4-γ}},\quad…
Symmetry breaking of extremals for the high order Caffarelli-Kohn-Nirenberg type inequalities: the singular case
Shengbing Deng, Xingliang Tian
Let us consider the following Caffarelli-Kohn-Nirenberg type inequality \begin{equation}\label{nsckn} \int_{\mathbb{R}^N}|x|^{-β}|\mathrm{div} (|x|^α\nabla u)|^2 \mathrm{d}x \geq \…
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\…