6 papers
Symmetry and uniqueness of the positive solution for the critical Hartree equation on the Heisenberg group
Shuijin Zhang, Jialin Wang, Yu Zheng +2
We apply the moving plane method in integral forms to classify the positive solutions of the critical Hartree equation on Heisenberg group \begin{equation}\label{0.1} -Δ_{\mathbb{H…
Quantitative stability of critical points for the nonlocal-Sobolev inequality in Heisenberg group
Shuijin Zhang, Jijie Xu, Jialin Wang
We investigate the quantitative stability of the nonlocal Sobolev inequality in Heisenberg group \begin{equation*}\label{non-Sobolev} C_{HL}(Q,μ) \left(\int_{\mathbb{H}^{n}}\int_{\…
Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications
Minbo Yang, Shuijin Zhang
We study the uniqueness and nondegeneracy of positive bubble solutions for the generalized energy-critical Hartree equation on the Heisenberg group , \begin{equatio…
On concentration of real solutions for fractional Helmholtz equation
Zifei Shen, Shuijin Zhang
This paper studies the nonlinear fractional Helmholtz equation \begin{equation}\label{main} (-Δ)^{s} u-k^{2} u=Q(x)|u|^{p-2}u, ~~\mathrm{in}~~\mathbb{R}^{N},~~N\geq3, \end{equation…
Complex and real valued solutions for fractoinal Helmholtz equation
Zifei Shen, Shuijin Zhang
In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation, By establishing the boundedness estimate for the resolvent of fraction…
On a critical Maxwell equation in nonlocal media
Minbo Yang, Weiwei Ye, Shuijin Zhang
In this paper, we study the existence of solutions for a critical time-harmonic Maxwell equation in nonlocal media. By introducing some suitable Coulomb spaces involving curl opera…