A5012209262- Advanced Mathematical Physics Problems
- Nonlinear Partial Differential Equations
- Navier-Stokes equation solutions
- Advanced Mathematical Modeling in Engineering
- Nonlinear Waves and Solitons
- Differential Equations and Boundary Problems
- Geometric Analysis and Curvature Flows
- Nonlinear Differential Equations Analysis
- Stability and Controllability of Differential Equations
- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Turbulent Flows
- Numerical methods in inverse problems
- Gas Dynamics and Kinetic Theory
- Ocean Waves and Remote Sensing
- Advancements in Semiconductor Devices and Circuit Design
- Spectral Theory in Mathematical Physics
- Silicon Carbide Semiconductor Technologies
- advanced mathematical theories
- Advanced Differential Equations and Dynamical Systems
- Geometry and complex manifolds
- Algebraic Geometry and Number Theory
- Coastal and Marine Dynamics
- Semiconductor materials and devices
University of Chinese Academy of Sciences
2019-2024
Peking University
2023-2024
Chinese Academy of Sciences
2020-2024
Academy of Mathematics and Systems Science
2022
Université Sorbonne Paris Nord
2021
Yeshiva University
2021
Beihang University
2018-2021
Jiangxi Science and Technology Normal University
2021
China Electronics Technology Group Corporation
2011
In this paper, we are concerned with the fractional and higher order H\'{e}non-Hardy type equations \begin{equation*} (-\Delta)^{\frac{\alpha}{2}}u(x)=f(x,u(x)) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n}, \mathbb{R}^{n}_{+} \text{or} \Omega \end{equation*} $n>\alpha$, $0<\alpha<2$ or $\alpha=2m$ $1\leq m<\frac{n}{2}$. We first consider typical case $f(x,u)=|x|^{a}u^{p}$ $a\in(-\alpha,\infty)$ $0<p<p_{c}(a):=\frac{n+\alpha+2a}{n-\alpha}$. By using method of scaling spheres,...
In this paper, we are concerned with the following equations \begin{equation*} \\\begin {cases} (-\Delta )^{m+\frac {\alpha }{2}}u(x)=f(x,u,Du,\cdots ), x\in \mathbb {R}^{n}, \\ u\in C^{2m+[\alpha ],\{\alpha \}+\epsilon }_{loc}\cap \mathcal {L}_{\alpha }(\mathbb {R}^{n}), u(x)\geq 0, {R}^{n} \end{cases}\end{equation*} involving higher-order fractional Laplacians. By introducing a new approach, prove super poly-harmonic properties for nonnegative solutions to above equations. Our theorem...
In this paper, we are mainly concerned with the physically interesting static Schrödinger--Hartree--Maxwell type equations $(-\Delta)^{s}u(x)=(\frac{1}{|x|^{\sigma}}\ast |u|^{p})u^{q}(x) \,\,\ {in} \,\,\, \mathbb{R}^{n}$ involving higher-order or fractional Laplacians, where $n\geq1$, $0<s:=m+\frac{\alpha}{2}<\frac{n}{2}$, $m\geq0$ is an integer, $0<\alpha\leq2$, $0<\sigma<n$, $0<p\leq\frac{2n-\sigma}{n-2s}$, and $0<q\leq\frac{n+2s-\sigma}{n-2s}$. We first prove super poly-harmonic...
.In this paper, without any assumption on \(v\) and under the extremely mild \(u(x)=O(|x|^{K})\) at \(\infty\) for some \(K\gg 1\) arbitrarily large, we prove classification of solutions to following conformally invariant system with mixed order exponentially increasing nonlinearity in \(\mathbb{R}^{2}:\begin {cases} (-\Delta )^{\frac {1}{2}}u(x)=e^{pv(x)}, \qquad x\in \mathbb {R}^{2}, \\ -\Delta v(x)=u^{4}(x), {R}^{2},\end {cases}\) where \(p\in (0,+\infty )\) , \(u\geq 0\) that satisfies...
Abstract In this paper, we are concerned with the Hardy–Hénon equations and . Inspired by Serrin Zou [25], prove Liouville theorems for nonnegative solutions to above (Theorem 1.1 Theorem 1.3), that is, unique solution is
In this paper, we first establish decay estimates for the fractional and higher-order H\'enon-Lane-Emden systems by using a nonlocal average integral estimates, which deduce result of non-existence. Next, apply method scaling spheres introduced in \cite{DQ2} to derive Liouville type theorem. We also construct an interesting example on super $\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).
In this paper, we consider the critical order Hardy-Hénon equations \begin{equation*} (-Δ)^{\frac{n}{2}}u(x)=\frac{u^{p}(x)}{|x|^{a}}, \,\,\,\,\,\,\,\,\,\,\, x \, \in \,\, \mathbb{R}^{n}, \end{equation*} where $n\geq4$ is even, $-\infty
In this paper, we are concerned with the non-critical higher order Lane-Emden-Hardy equations \begin{equation*} (-\Delta)^{m}u(x)=\frac{u^{p}(x)}{|x|^{a}} \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n} \end{equation*} $n\geq3$, $1\leq m<\frac{n}{2}$, $0\leq a<2m$, $1<p<\frac{n+2m-2a}{n-2m}$ if a<2$, and $1<p<\infty$ $2\leq a<2m$. We prove Liouville theorems for nonnegative classical solutions to above (Theorem \ref{Thm0}), that is, unique solution is $u\equiv0$. As an application,...
In this paper, we construct smooth travelling counter-rotating vortex pairs with circular supports for the generalized surface quasi-geostrophic equation. These are analogues of Lamb dipoles two-dimensional incompressible Euler The solutions obtained by maximization energy over some appropriate classes admissible functions. We establish uniqueness maximizers and compactness maximizing sequences in our variational setting. Using these facts, further prove orbital stability gSQG
In this paper, we aim to introduce the method of scaling spheres (MSS) as a unified approach Liouville theorems on general domains in $\mathbb R^n$, and apply it establish arbitrary unbounded or bounded MSS applicable for ($\leq n$-th order) PDEs integral equations without translation invariance with singularities. The set includes any generalized radially convex complementary sets their closures, which is invariant under Kelvin transforms maximal collection simply connected such that works....