6 papers
Asymptotic behavior of solutions for the nonlinear Hartree equation involving the fractional Laplacian
Natalino Borgia, Silvia Cingolani, Minbo Yang +1
In this paper, we investigate the nonlocal problem \begin{equation*}\left\lbrace \begin{aligned} &A_{s} u=(|x|^{-(n-2s)}\ast u^{2_{s}^{\sharp}-1-ε})u^{2_{s}^{\sharp}-2-ε} \quad\q…
Qualitative properties of blowing-up solutions of nonlinear elliptic equations with critical Sobolev exponent
Minbo Yang, Shunneng Zhao
In this paper, we are concerned with the critical elliptic equation \begin{equation}\label{kx} \left\lbrace\begin{aligned} &-Îu=u^{p}+εκ(x)u^{q}\quad\hspace{2mm} \mbox{in}~~Ω,…
Qualitative properties of single blow-up solutions for nonlinear Hartree equation with slightly subcritical exponent
Alessandro Cannone, Silvia Cingolani, Minbo Yang +1
In this paper, we study the qualitative properties of single blow-up solutions to the nonlocal equations with slightly subcritical exponents \begin{equation*} -Îu=(|x|^{-(n-2)}\as…
Asymptotic behavior of least energy solutions to the nonlinear Hartree equation near critical exponent
Silvia Cingolani, Minbo Yang, Shunneng Zhao
In this paper, we study that the nearly critical nonlocal problem \begin{equation*} \left\lbrace \begin{aligned} &-Îu=(|x|^{-{(n-2)}}\ast u^{p-ε})u^{p-1-ε} \quad \mbox{in}\quad…
Remainder terms, profile decomposition and sharp quantitative stability in the fractional nonlocal Sobolev-type inequality with
Qikai Lu, Minbo Yang, Shunneng Zhao
In this paper, we study the following fractional nonlocal Sobolev-type inequality \begin{equation*} C_{HLS}\bigg(\int_{\mathbb{R}^n}\big(|x|^{-μ} \ast |u|^{p_s}\big)|u|^{p_s} dx\b…
Stability estimates for critical points of a nonlocal Sobolev-type inequality
Minbo Yang, Shunneng Zhao
In this paper, we study the stability of the following nonlocal Soblev-type inequality \begin{equation*} C_{HLS}\big(\int_{\mathbb{R}^n}\big(|x|^{-μ} \ast u^{p}\big)u^{p} dx\big)^…