52 citations · 293 across the 36 of their papers we have counts for
36 papers
Global existence for quasilinear wave equations on hyperbolic space
Wei Dai, Chengbo Wang
The main purpose of this paper is to study the global solvability for a general class of quasilinear shifted wave equations on hyperbolic spaces, for smooth initial data with small…
Method of scaling spheres: Liouville theorems in inner or outer (unbounded or bounded) generalized radially convex domains, blowing-up analysis on domains with not necessarily boundary and other applications
Wei Dai, Guolin Qin
In this paper, we aim to introduce the method of scaling spheres (MSS) as a unified approach to Liouville theorems on general domains in , and apply it to establish Li…
The Maxwell-Klein-Gordon equation with scattering data
Wei Dai, He Mei, Dongyi Wei +1
It has been shown in [Yang-Yu 2019] that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space decay lik…
The global behaviors for defocusing wave equations in two dimensional exterior region
Wei Dai
We study the defocusing semilinear wave equation in with the Dirichlet boundary condition, where is a star-s…
Uniform a priori estimates for -th order Lane-Emden system in with
Wei Dai, Leyun Wu
In this paper, we establish uniform a priori estimates for positive solutions to the (higher) critical order superlinear Lane-Emden system in bounded domains with Navier boundary c…
A Generic Closed-form Optimal Step-size for ADMM
Yifan Ran, Wei Dai
In this work, we present a generic step-size choice for the ADMM type proximal algorithms. It admits a closed-form expression and is theoretically optimal with respect to a worst-c…
On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents
Wei Dai, Jingze Fu
In this paper, we investigate various properties (e.g., nonexistence, asymptotic behavior, uniqueness and integral representation formula) of positive solutions to nonlinear tri-ha…
Classification of solutions to conformally invariant systems with mixed order and exponentially increasing or nonlocal nonlinearity
Wei Dai, Guolin Qin
In this paper, without any assumption on and under extremely mild assumption at for some arbitrarily large, we prove classification of soluti…
Long time existence for semilinear wave equations with the inverse-square potential
Wei Dai, Daoyuan Fang, Chengbo Wang
In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analy…
A reduction approach to silting objects for derived categories of hereditary categories
Wei Dai, Changjian Fu
Let be a hereditary abelian category over a field with finite dimensional and spaces. It is proved that the bounded deri…
Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times
Wei Dai, Daoyuan Fang, Chengbo Wang
By assuming certain local energy estimates on -dimensional asymptotically flat space-time, we study the existence portion of the \emph{Strauss} type wave system. Firstly we…
Existence and symmetry of solutions to 2-D Schrödinger-Newton equations
Daomin Cao, Wei Dai, Yang Zhang
In this paper, we consider the following 2-D Schrödinger-Newton equations \begin{eqnarray*} -Δu+a(x)u+\fracγ{2π}\left(\log(|\cdot|)*|u|^p\right){|u|}^{p-2}u=b{|u|}^{q-2}u \qquad \t…
Sharp reversed Hardy-Littlewood-Sobolev inequality with extended kernel
Wei Dai, Yunyun Hu, Zhao Liu
In this paper, we prove the following reversed Hardy-Littlewood-Sobolev inequality with extended kernel \begin{equation*} \int_{\mathbb{R}_+^n}\int_{\partial\mathbb{R}^n_+} \frac{x…
Self-similar solutions of energy-supercritical focusing wave equations in all dimensions
Wei Dai, Thomas Duyckaerts
In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy super-critical semi-linear wave equations \be…
Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications
Wei Dai, Guolin Qin
In this paper, we establish various maximum principles and develop the method of moving planes and the sliding method (on general unbounded domains) for equations involving the uni…
Direct methods for pseudo-relativistic Schrödinger operators
Wei Dai, Guolin Qin, Dan Wu
In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo…
Existence and axial symmetry of minimal action odd solutions for 2-D Schrödinger-Newton equation
Yang Zhang
We consider the following 2-D Schrödinger-Newton equation \begin{eqnarray*} \begin{cases} -Δu+u=w|u|^{p-1}u \\ -Δw=2 π|u|^p \end{cases}\text{in} \; \mathbb{R}^2 \end{eqnarray*} for…
Classification of nonnegative solutions to static Schrödinger-Hartree-Maxwell type equations
Wei Dai, Zhao Liu, Guolin Qin
In this paper, we are mainly concerned with the physically interesting static Schrödinger-Hartree-Maxwell type equations \begin{equation*} (-Δ)^{s}u(x)=\left(\frac{1}{|x|^σ}\ast |u…
Blow-up for Strauss type wave equation with damping and potential
Wei Dai, Hideo Kubo, Motohiro Sobajima
We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. B…
Uniform a priori estimates for positive solutions of higher order Lane-Emden equations in
Wei Dai, Thomas Duyckaerts
In this paper, we study the existence of uniform a priori estimates for positive solutions to Navier problems of higher order Lane-Emden equations \begin{equation*} (-Δ)^{m}u(x)=u^…
Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians
Daomin Cao, Wei Dai, Guolin Qin
In this paper, we are concerned with equations \eqref{PDE} involving higher-order fractional Laplacians. By introducing a new approach, we prove the super poly-harmonic properties…
Liouville type theorems for elliptic equations with Dirichlet conditions in exterior domains
Wei Dai, Guolin Qin
In this paper, we are mainly concerned with the Dirichlet problems in exterior domains for the following elliptic equations: \begin{equation}\label{GPDE0} (-Δ)^{\fracα{2}}u(x)=f(x,…
Classification of nonnegative solutions to static Schrödinger-Hartree and Schrödinger-Maxwell equations with combined nonlinearities
Wei Dai, Zhao Liu
In this paper, we are concerned with static Schrödinger-Hartree and Schrödinger-Maxwell equations with combined nonlinearities. We derive the explicit forms for positive solution $…
Liouville type theorem for critical order Hénon-Lane-Emden type equations on a half space and its applications
Wei Dai, Guolin Qin
In this paper, we are concerned with the critical order Hénon-Lane-Emden type equations with Navier boundary condition on a half space : \begin{equation}\label{NPDE…