7 citations · 15 across the 8 of their papers we have counts for
8 papers
Existence of global solutions for the nonlocal derivation nonlinear Schrödinger equation by the inverse scattering transform method
Yuan Li, Xinhan Liu, Engui Fan
We address the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schrödinger equation in weighted Sobolev space $H^{2}(\ma…
Blowup dynamics for mass critical Half-wave equation in 2D
Vladimir Georgiev, Yuan Li
We consider the half-wave equation in two dimensions. For the initial data , , we obtain the non-radia…
On mass - critical NLS with local and non-local nonlinearities
Vladimir Georgiev, Yuan Li
We consider the following nonlinear Schrödinger equation with the double -critical nonlinearities \begin{align*} iu_t+Δu+|u|^\frac{4}{3}u+μ\left(|x|^{-2}*|u|^2\right)u=0\ \ \…
Blowup dynamics for Mass Critical Half-wave equation in 3D
Vladimir Georgiev, Yuan Li
We consider the half-wave equation in three dimension and in the mass critical. For initial data with…
Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations
Mostafa Fazly, Yuan Li
We study the quasilinear elliptic equation \begin{equation*} -Qu=e^u \ \ \text{in} \ \ Ω\subset \mathbb{R}^{N} \end{equation*} where the operator , known as Finsler-Laplacian (o…
Nondispersive solutions to the mass critical half-wave equation in two dimensions
Vladimir Georgiev, Yuan Li
We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we p…
Boson Stars with Long-range Perturbations
Qingxuan Wang, Binhua Feng, Yuan Li
We consider the Boson star equation with long-range perturbation given by $$i\partial_t ψ=\sqrt{-\triangle+m^2}\,ψ+β(\frac{1}{|x|^α}\ast |ψ|^2)ψ-(\frac{1}{|x|}\ast |ψ|^2)ψ \ \ \tex…
Concentration Behavior of Nonlinear Hartree-type Equation with almost Mass Critical Exponent
Yuan Li, Dun Zhao, Qingxuan Wang
We study the following nonlinear Hartree-type equation \begin{equation*} -Δu+V(x)u-a(\frac{1}{|x|^γ}\ast |u|^2)u=λu,~\text{in}~\mathbb{R}^N, \end{equation*} where , ,…