北京师范大学 非线性分析研讨会
北京师范大学
非线性分析研讨会（线上）
会议时间：2021年10月30日 星期六
腾讯会议 ID：629 509 075 会议密码：211030
邀请专家：
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陈化 （武汉大学）
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罗鹏（华中师范大学）
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戴蔚（北航大学）
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孙春友（兰州大学）
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丁彦恒（中国科学院）
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王博（北京理工大学）
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窦井波（陕西师范大学）
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严树森（华中师范大学）
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郭玉霞（清华大学）
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张程翔（北京师范大学）
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郭宗明（河南师范大学）
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周焕松（武汉理工大学）
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李永青（福建师范大学）
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学术委员会：保继光 曹道民 李岩岩 王志强
组委会：唐仲伟 熊金钢 张程翔
资助：“双一流”团队项目、国家自然科学基金
会议日程
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2021年10月30日 上午
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时间
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题目
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报告人
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主持人
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8:50-9:00
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开幕式：王恺顺院长致辞
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熊金钢
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9:00-9:40
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非线性量子力学系统的几个结果
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丁彦恒
中国科学院数学与系统科学研究院
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周焕松
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9:45-10:25
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Existence and multiplicity of solutions to semilinear Dirichlet problem for subelliptic operator with a free perturbation
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陈化
武汉大学
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10:40-11:20
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 isoperimetric inequality on the unit disk
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窦井波
陕西师范大学
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郭宗明
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11:25-12:05
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Qualitative analysis of positive solutions to the Lane-Emden problem in dimension two
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罗鹏
华中师范大学
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2021年10月30日 下午
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时间
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题目
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报告人
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主持人
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14:00-14:40
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On the stable critical points
for the Robin functions
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严树森
华中师范大学
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郭玉霞
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14:45-15:25
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Infinite-dimensional dissipative dynamical systems and its attractors
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孙春友
兰州大学
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15:40-16:20
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On properties of nonnegative solutions to equations involving nonlocal operators
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戴蔚
北京航空航天大学
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李永青
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16:25-17:05
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On the  -Nirenberg problem
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王博
北京理工大学
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17:10-17:50
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Nonlinear elliptic equations of sublinearity: qualitative behavior of solutions
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张程翔
北京师范大学
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唐仲伟
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报告题目和摘要
Existence and multiplicity of solutions to semilinear Dirichlet problem for subelliptic operator with a free perturbation
陈化
武汉大学
Abstract：In this talk, we shall report some results on existence and multiplicity for Dirichlet problem of semilinear subelliptic equation with free perturbation term. By using the degenerate Rellich-Kondrachov compact embedding theorem, precise lower bound estimates of Dirichlet eigenvalues for the finitely degenerate elliptic operator and minimax method, we can obtain the existence and multiplicity of weak solutions for the problem.
On properties of nonnegative solutions to equations
involving nonlocal operators
戴蔚
北京航空航天大学
Abstract：In this talk, we will introduce various maximal principles and the direct moving planes and sliding methods for equations involving the (nonlocal) Pseudo-relativistic Schrödinger Operators. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the Pseudo-relativistic Schrödinger Operators in bounded or unbounded domains (e.g., coercive epigraph and epigraph), including the equations with De Giorgi type nonlinearities. Various properties of nonneagtive solutions to equations involving the (uniformly elliptic) nonlocal Bellman operator and the higher-order fractional Laplacians will also be talked.
非线性量子力学系统的几个结果
丁彦恒
中国科学院数学与系统科学研究院
摘要：报告利用变分方法研究非线性(相对论)量子力学系统的一些新进展：
★ 非线性Dirac方程和非线性Klein-Gordon方程的耦合,
★ 非线性Dirac方程和非线性Maxwell方程的耦合,
包括解的存在性、指数衰减性与集中现象；以及Dirac方程的非相对论极限、凹凸非线性问题的多解性，等。
isoperimetric inequality on the unit disk
窦井波
陕西师范大学
Abstract：In this talk, we obtain a sharp isoperimetric inequality on the unit disk for 
functions and classify all extremal functions. The original isoperimetric inequality was obtained in 1921 by Carleman for analytic functions on the unit ball. This is a joint work with Meijun Zhu.
Qualitative analysis of positive solutions to the Lane-Emden problem in dimension two
罗鹏
华中师范大学
Abstract： In this talk, we are concerned with the Lane-Emden problem. Improving some known asymptotic estimates on the solutions, we prove the non-degeneracy and local uniqueness of the multi-spikes positive solutions for general domains. Our methods mainly use ODE's theory, various local Pohozaev identities, blow-up analysis and the properties of Green's function. This is a series of work jointed with Massimo Grossi, Isabella Ianni and Shusen Yan.
Infinite-dimensional dissipative dynamical systems and its attractors
孙春友
兰州大学
Abstract：This talk will focus on our progress on the attractors of infinite-dimensional dissipative dynamical systems, and its applications to some dissipative wave-type equations and reaction-diffusion equations
On the 
-Nirenberg problem
王博
北京理工大学
Abstract：In this talk, I will present some recent results on the problem of prescribing -curvature for a conformal metric on the standard sphere. Compactness, non-compactness, existence and non-existence will be concerned. This is a joint work with YanYan Li and Luc Nguyen.
On the stable critical points for the Robin functions
严树森
华中师范大学
Abstract：I will talk about the stable critical points for the Robin functions. The focus will be on the effect of the domain topology and the domain shape on the existence of such critical points. Such problem play an important role on many elliptic problems, such as the de-singularization problems for incompressible Euler flow in two dimensional domains, the bubbling solutions with critical growth in higher dimensions.
Nonlinear elliptic equations of sublinearity: qualitative behavior of solutions
张程翔
北京师范大学
Abstract：We study existence, uniqueness and qualitative property of solutions for a class of nonlinear elliptic equations of sublinearity. We also study the asymptotic behavior of ground state solution for sublinear equations in 
and give estimates for radius of its support set as various parameters involved including the sublinearity power approaching to the limiting cases. This is a joint work with Prof. Norihisa Ikoma, Kazunaga Tanaka, and Zhi-Qiang Wang.
