大连理工大学数学科学学院
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2018年非线性泛函分析及应用学术会议

2018年06月07日 14:45  点击:[]

 

 

2018年“非线性泛函分析及应用”学术会议

 

 

举办单位: 大连理工大学数学科学学院

2018.6.22-25 大连

 

 

“非线性泛函分析及应用”学术会议

(会议须知)

 

“非线性泛函分析及应用”学术会议旨在加强国内非线性分析及其相关领域学者之间的沟通,交流各自的最新研究成果,促进彼此间的合作,探讨非线性分析中的前沿问题,推动我国非线性分析研究的健康发展。会议主题包括非线性泛函分析的理论及其在各相关领域中的应用。本次会议拟定于2018622日至25日(22日报到,25日离会)在大连理工大学举行,会议由大连理工大学数学科学学院承办。具体事宜如下:

一、会议组委会;

  李风泉,电话:15164005929   E-mailfqli@dlut.edu.cn

代国伟,电话:13898436901   E-maildaiguowei@dlut.edu.cn

段犇,  电话:13610844661   E-mailbduan@dlut.edu.cn

房祥东,电话:15840980504   E-mailfangxd0401@dlut.edu.cn

禹芳,  电话:15898102863   E-mailfangyu@dlut.edu.cn

二、会议日期:

2018622-25日,22日报到(大连星海高尔夫酒店中心大厅),25日离会

三、会议地点:大连星海高尔夫酒店

四、会议住宿:大连星海高尔夫酒店

五、会议费用:本次会议不收取注册费,食宿统一安排,交通费用自理

六、会议联系人:代国伟,电话:13898436901

                    E-maildaiguowei@dlut.edu.cn

日程安排

6月23日上午

大会报告(地点:三楼会议室)

 

 

  人 及  题 

主持人

23

7:50-8:00

照相:全体代表

于化东

8:10-8:20

开幕式:卢玉峰  李树杰

8:20-9:05

李树杰:变分理论中的环绕方法

卢玉峰 

9:05-9:50

彭双阶:Construction of  solutions via local Pohozaev identities

9:50-10:00

茶歇

10:00-10:45

丁彦恒:待定

周焕松

10:45-11:30

邹文明:待定

 

11:30-13:30

午餐(一楼商务,自助)

 

 

 

 

 

 

6月23日下午

组报告一(地点:三楼会议室)

 

 

  人 及  题 

主持人

23

13:50-14:20

韩丕功:Long-time  behavior for the nonstationary Navier-Stokes flows in L^1 space

彭双阶

14:20-14:50

唐仲伟:Multi-bump bound  states for a Schrodinger system

14:50-15:20

潘洪京:Bifurcation  results for prescribed mean curvature equations in bounded domains

15:20-15:50

常小军:Existence and  multiplicity of sign-changing solutions of fractional p-Laplacian problems

15:50-16:00

茶歇

 

16:00-16:30

李翀:The Fučík spectrum of Schrodinger  operator and the existence of four solutions of Schrödinger equations with jumping  nonlinearities

王志强

16:30-17:00

徐露:Hadamard  variational formulas for two functionals and its application to related  Minkowski problem

17:00-17:30

张彬林:Existence and  blow-up of solutions for fractional Kirchhoff diffusion problems

 

18:00

晚宴(一楼西餐厅)

 

 

 

 

 

6月23日下午

组报告二(地点:四楼会议室)

 

 

  人 及  题 

主持人

23

13:50-14:20

张志军:Boundary  behavior of large solutions to several classes  of (fully) nonlinear  elliptic equations with weights

邹文明

14:20-14:50

陈志杰: On radial  solutions to the Chern-Simons system

14:50-15:20

李科学:Explosive  solutions of parabolic stochastic partial differential equations with Levy  noise

15:20-15:50

王元恒:The modified  viscosity implicit rules for Lipschitzian asymptotically pseudocontractive  mappings in Banach spaces

15:50-16:00

茶歇

 

16:00-16:30

杨敏波:Existence of  solutions for critical Choquard type equation in R^2

张志涛

16:30-17:00

邢瑞香:Symmetry-breaking bifurcations and  non-axisymmetric solutions for free boundary problems modeling tumor growth

17:00-17:30

余晓辉:Liouville Type Theorem for Some Nonlocal  Elliptic Equations

 

18:00

晚宴(一楼西餐厅)

 

 

 

 

 

6月24日上午

大会报告(地点:三楼会议室)

 

 

  人 及  题 

主持人

24

8:00-8:45

王志强:A class of quasilinear elliptic  equations via a regularization approach

李树杰

8:45-9:30

张志涛:Some new results  on Henon-Lane-Emden conjecture and Schrodinger systems

9:30-9:40

茶歇

 

9:50-10:35

陈文雄:A Hopf Lemma for  the Fractional p-Laplacian

 

丁彦恒

10:35-11:20

唐春雷:Ground state  sign-changing solutions for a class of subcritical Choquard equations with a  critical pure power nonlinearity

11:30-13:30

午餐(一楼中餐厅,自助)

24

14:00-18:00

自由讨论

18:00

晚餐(一楼中餐厅)

 

 

 

 

 

 

 

 

参会代表名单

(按学校拼音排序)

 

姓名

学校

E-mail

蒋美跃

北京大学

mjiang@math.pku.edu.cn

唐仲伟

北京师范大学

tangzw@bnu.edu.cn

李麟

重庆工商大学

lilin420@gmail.com

代国伟

大连理工大学

daiguowei@dlut.edu.cn

段犇

大连理工大学

bduan@dlut.edu.cn

房祥东

大连理工大学

fangxd0401@dlut.edu.cn

韩志清

大连理工大学

hanzhiq@dlut.edu.cn

李风泉

大连理工大学

fqli@dlut.edu.cn

卢玉峰

大连理工大学

lyfdlut@dlut.edu.cn

禹芳

大连理工大学

fangyu@dlut.edu.cn

郑斯宁

大连理工大学

snzheng@dlut.edu.cn

周岩

大连理工大学

yzhou_math@163.com

张娜

大连理工大学

zhangn_math@163.com

邢媛媛

大连理工大学

yyx_math@163.com

罗华

东北财经大学

luohua@dufe.edu.cn

常小军

东北师范大学

changxj100@nenu.edu.cn

张福保

东南大学

zhangfubao@seu.edu.cn

陈建清

福建师范大学

jqchen@fjnu.edu.cn

曹道民

广州大学/中国科学院

dmcao@amt.ac.cn

崔仁浩

哈尔滨师范大学

renhaocui@163.com

张晶

哈尔滨师范大学

zhjmath11@163.com

李晓军

河海大学

lixjun05@hhu.edu.cn

郭宗明

河南师范大学

gzm@htu.cn

张彬林

黑龙江工程学院

zhbinlin@126.com

黄勇

湖南大学

huangyong@hnu.edu.cn

徐露

湖南大学

xulu@hnu.edu.cn

潘洪京

华南师范大学

panhj@m.scnu.edu.cn

彭双阶

华中师范大学

sjpeng@mail.ccnu.edu.cn

王春花

华中师范大学

chunhuawang@mail.ccnu.edu.cn

王俊

江苏大学

wangmath2011@126.com

刘笑颖

江苏师范大学

xuzhliuxy@163.com

杨健夫

江西师范大学

jfyang_2000@yahoo.com

程锡友

兰州大学

chengxy@lzu.edu.cn

李万同

兰州大学

wtli@lzu.edu.cn

刘都超

兰州大学

liudch@lzu.edu.cn

陈文雄

美国Yehsiva  大学

wchen@yu.edu

钟承奎

南京大学

ckzhong@nju.edu.cn

张吉慧

南京师范大学

zhangjihui@njnu.edu.cn

陈志杰

清华大学

zjchen2016@mail.tsinghua.edu.cn

章梅荣

清华大学

mzhang@math.tsinghua.edu.cn

邹文明

清华大学

wzou@math.tsinghua.edu.cn

杜新生

曲阜师范大学

duxinsheng1977@163.com

蒋继强

曲阜师范大学

qfjjq@163.com

李傅山

曲阜师范大学

fushan99@163.com

毛安民

曲阜师范大学

maoam@163.com

钱爱侠

曲阜师范大学

qaixia@amss.ac.cn

王培合

曲阜师范大学

peihewang@hotmail.com

赵增勤

曲阜师范大学

zqzhaoy@163.com

胡锡俊

山东大学

xjhu@sdu.edu.cn

张晓燕

山东大学

zxysd@sdu.edu.cn

余晓辉

深圳大学

Xiaohui.yu@szu.edu.cn

刘兆理

首都师范大学

zliu@mail.cnu.edu.cn

张世清

四川大学

zhangshiqing@msn.com

李德生

天津大学

lidsmath@tju.edu.cn

Zhi-Qiang Wang

Utah State  University 天津大学

zhi-qiang.wang@usu.edu

张志军

烟台大学

zhangzj@ytu.edu.cn

赵富坤

云南师范大学

fukunzhao@163.com

王征平

武汉理工大学

zpwang@whut.edu.cn

张贻民

武汉理工大学

zhangym802@126.com

周焕松

武汉理工大学

hszhou@whut.edu.cn

李科学

西安交通大学

kxli@mail.xjtu.edu.cn

马如云

西北师范大学

mary@nwnu.edu.cn

徐嘉

西北师范大学

xujia@nwnu.edu.cn

唐春雷

西南大学

tangcl@swu.edu.cn

沈自飞

浙江师范大学

szf@zjnu.edu.cn

王元恒

浙江师范大学

yhwang@zjnu.cn

杨敏波

浙江师范大学

mbyang@zjnu.edu.cn

丁彦恒

中国科学院

dingyh@math.ac.cn

韩丕功

中国科学院

pghan@amss.ac.cn

李翀

中国科学院

lichong@amss.ac.cn

李树杰

中国科学院

lisj@math.ac.cn

张志涛

中国科学院

zzt@math.ac.cn

孙义静

中国科学院大学

yjsun@ucas.edu.cn

麻希南

中国科学技术大学

xinan@ustc.edu.cn

郭玉劲

中科院武汉物理与数学研究所

yjguo@wipm.ac.cn

邢瑞香

中山大学

xingrx@mail.sysu.edu.cn

贺小明

中央民族大学

xmhe923@muc.edu.cn

 

 

 

 

 

 

 

报告题目和摘要

(按姓氏拼音排序)

 

(1)常小军 东北师范大学

题目Existence and multiplicity of sign-changing solutions of fractional p-Laplacian problems

摘要In this talk, we report some recent results on the sign-changing  solutions of fractional p-Laplacian problems. By applying the method of invariant sets of descending flow and minimax theory, we obtain the existence and multiplicity of sign-changing solutions of the fractional p-Laplacian problems. In addition, by using the Nehari manifold method, we prove  that the  problem admits one least energy sign-changing solution, and its energy exceeds twice the least energy solutions.

 

(2)陈文雄美国Yehsiva大学

题目A Hopf Lemma for the Fractional p-Laplacian

摘要In this talk, we will introduce a Hopf lemma for the fractional Laplacian and for the fractional p-Laplacian. We will explain the difference between these non-local operators and the usual local differential operators; and we will illustrate the idea of proofs of these lemmas by constructing sub-solutions.

 

(3)陈志杰清华大学

题目 On radial solutions to the Chern-Simons system

摘要 In this talk, I will introduce the Chern-Simons system, a second order nonlinear elliptic system in R2. Such systems have presented many challenging problems for analysts. I will talk about the existence of radial non-topological solutions with prescribed asymptotic behaviors at infinity. This is based on joint work with Professor Chang-Shou Lin.

 

(4)丁彦恒 中国科学院

A

 

(5)韩丕功     中国科学院

题目 Long-time behavior for the nonstationary Navier-Stokes flows in L^1 space

摘要In this talk, we consider the large time decay for the Navier-Stokes flows in L^1(\mathbb{R}^n_+). Using the Stokes solution formula, we find a crucial and new estimate for the Stokes flow in L^1(\mathbb{R}^n_+), which plays a fundamental role in studying the time L^1-behavior for the Navier-Stokes equations. In addition, we decompose the operator into two parts, and reduce its unboundedness to establish an L^1 estimate for an elliptic problem with Neumann boundary condition, which is overcome by using the weighted estimates of the Gaussian kernel's convolution.

 

(6)李翀中国科学院

题目The Fučík spectrum of Schrödinger operator and the existence of four solutions of Schrödinger equations with jumping nonlinearities

摘要This paper contains the existence of four solutions of Schrödinger equations with jumping nonlinearities. The proof procedure is supported by a lot of new results. Initially, a consequence is rendered as a minimax principle on , which allows us to achieve the feasibility verification of the (PS) condition. Furthermore, the constructions of minimal and maximal curves of Fučík spectrum in (see the introduction for the definition of ) warrant a thorough investigation. That we encounter some thorny problems is largely due to the absence of compact embedding and the appearance of essential spectrum. Based on a nontrivial argument, we can compute critical groups of homogeneous functional at zero ifis free of Fučík spectrum and . This together with convexity and concavity offers a detailed description of the two curves by a series of sophisticated tricks. Additionally, we present a new version of Morse theory in view of the fact that classical version doesn’t work directly for weak smooth functional on. Finally, we prove a weak maximum principle for, which serves as a tool to get a critical point in positive and negative cone respectively and also compute critical groups of critical points of mountain pass type. With the help of above preparations, we attain the ultimate aim by Morse inequalities and various exact homology sequences.

 

(7)李科学西安交通大学

题目 Explosive solutions of parabolic stochastic partial differential equations with Levy noise

摘要 We study the explosive solutions to a class of parabolic stochastic semilinear differential equations driven by a Levy type noise. The sufficient conditions are presented to guarantee the existence of a unique positive solution of the stochastic partial differential equation under investigation. Moreover, we show that positive solutions will blow up in finite time in mean Lp-norm sense, provided that the initial data, the nonlinear term and the multiplicative noise satisfies some conditions. Several examples are presented to illustrate the theory. Finally, we establish a global existence theorem based on a Lyapunov functional and prove that a stochastic Allen-Cahn equation driven by Levy noise has a global solution.

 

(8)李树杰     中国科学院

题目 变分理论中的环绕方法

摘要 本报告主要是介绍变分理论中的环绕方法。该方法中最早而且众所周知的工作就是山路定理以及后来发展起来的鞍点、广义鞍点定理等。这里介绍一种与Nehari流形结构有关的Nehari型环绕,并将它应用于半线性椭圆方程和强不定问题中,得到一系列解的存在性。

 

(9)潘洪京华南师范大学

题目 Bifurcation results for prescribed mean curvature equations in bounded domains

摘要 Bifurcation for prescribed mean curvature equations in one dimension has been intensively investigated in recent years, and a striking phenomenon discovered is that the length of the interval may affect the shapes of bifurcation curves. However, to our best knowledge, no such results are known in higher dimensions. In this talk, we are concerned with a class of prescribed mean curvature equations in bounded domains of R^N with general nonlinearities f satisfying f(0) = 0 and f’(0) > 0. We establish some new results that the size of the domain can effect bifurcation directions. In contrast, this phenomenon does not occur for the corresponding semilinear problems. This is a joint work with Ruixiang Xing (Sun Yat-sen University).

 

(10) 彭双阶 华中师范大学

题目Construction of solutions via local Pohozaev identities

摘要When constructing solution concnetrating on the critical points of potential functions for the problems with Sobolev critical exponent, how to decide the position of the bubbles is usual difficult, and no arguments are effective. In this talk, we will introduce an new augrment based on the local Pohozaev identities which works well for this type of problem.

 

(11)唐春雷   西南大学

题目Ground state sign-changing solutions for a class of subcritical Choquard equations with a critical pure power nonlinearity

摘要In this talk, we discuss work on the existence of ground state sign-changing solutions for a class of Choquard equations. Using the sign-changing Nehari manifold, we prove the existence of ground state sign-changing solutions for a class of subcritical Choquard equations with a critical pure power nonlinearity. This result can be also regarded as the complementary work of Ghimenti and Van Schaftingen (2016), Van Schaftingen and Xia (2017).

 

(12)唐仲伟北京师范大学

题目Multi-bump bound states for a Schr\"{o}dinger system

摘要In this talk, we present some results for the existence of Multi-bump solutions for the n \times n system of coupled Schr\"{o}dinger equations. This is a joint work with Dr Lushun Wang  and professor Marcello Lucia.

 

(13)杨敏波   浙江师范大学

题目Existence of solutions for critical Choquard type equation in R^2

摘要In this talk we are going to introduce some existence results for the critical Choquard type eqtion in R^2, by assume that the nonlinearity is of critical growth in the sense of weighted Trudinger-Morser inequality, we are able to prove the existence results by using variational methods.

 

(14)余晓辉   深圳大学

题目Liouville Type Theorem for Some Nonlocal Elliptic Equations

摘要In this talk, we will introduce some Liouville theorems for elliptic equations with nonlocal nonlinearities. Because of the nonlocal nonlinearities, it is not easy to apply the moving plane method directly. Moreover, since the nonlinearity is only assumed to be continuous, the classical maximum principles cannot be applied. To overcome our difficulties, we turn the equation into an integral-differential system, then we use the moving plane method in an integral form to prove our results.

 

(15)王元恒   浙江师范大学

题目The modified viscosity implicit rules for Lipschitzian asymptotically pseudocontractive mappings in Banach spaces

摘要The aim of this paper is to establish the modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudo- contractive mappings in Banach spaces. The strong convergence theorems of the rules are proved under certain assumptions imposed on the sequences of parameters. As an application, we apply our main results to solve some variational inequality in Banach spaces, provided T is asymptotically regular. Our results extend the previous known results from Hilbert spaces to Banach spaces and from nonexpensive mappings to asymptotically pseudo-contractive mappings.

 

(16) Zhi-Qiang Wang 天津大学/美国Utah State大学

题目 A class of quasilinear elliptic equations via a regularization approach

摘要For a class of quasilinear elliptic problems including the modified nonlinear Schr\"odinger type equations, which lack both smoothness and compactness in the variational formulations, we develop a regularization approach for the existence theory. This allows us to overcome difficulties of both smoothness and compactness issues involved. By establishing convergence results we obtain existence and multiplicity results for the quasilinear equations.

 

(17)邢瑞香   中山大学

题目Symmetry-breaking bifurcations and non-axisymmetric solutions for free boundary problems modeling tumor growth

摘要We study a free boundary problem (FBP) modeling solid tumor growth. The problem contains a parameter \mu. It is well known in Friedman-Fontelos (2003) and Friedman-Hu (2008) that the problem admit a unique radially symmetric solution with free boundary r=R_S and a sequence of symmetry-breaking branches of non-radially solutions bifurcating from an increasing sequence \mu= \mu_l(R_S) (l=2,4,6,\cdots) with free boundary r= R_S + \varepsilon Y_{l,0}(\theta) + O(\varepsilon^2), where Y_{l,0} is the spherical harmonic of mode (l,0). This type of symmetry-breaking solution is in fact axisymmetric. No non-axisymmetric solutions are known. Using equivariant bifurcation analysis and group-theoretic ideas, we prove that the existence of a plethora of non-axisymmetric solutions. The approach also applies to many other FBPs arising in tumor-growth or protocell models and establishes new symmetry-breaking results.

 

(18)徐露湖南大学

题目Hadamard variational formulas for two functionals and its application to related Minkowski problem

摘要this paper, we pose two kinds of Minkowski problems involving the p-Laplacian operator. The Hadamard variational formulas for some p-Laplacian functionals are obtained. A good application is to prove symmetry results for solutions to some overdetermined problems of p-Laplacian equations.

 

(19)张彬林黑龙江工程学院

题目Existence and blow-up of solutions for fractional Kirchhoff diffusion problems

摘要In this talk, we study a diffusion model of Kirchhoff-type driven by fractional Laplace operator. Under some appropriate conditions, the local existence of nonnegative solutions is obtained by employing the Galerkin method. Then, by means of a differential inequality technique, we prove that the local nonnegative solutions blow-up in finite time with arbitrary negative initial energy and suitable initial values. Moreover, we give an estimate for the lower and upper bounds of the blow-up time. The main feature of our problems is that the Kirchhoff function could be zero at zero.

 

(20)张志军   烟台大学

题目Boundary behavior of large solutions to several classes  of (fully) nonlinear elliptic equations with weights

摘要In this talk we give the exact boundary behavior of large solutions to several classes of (fully) nonlinear elliptic equations A(u) =b(x)f(u), \ \ x\in \Omega, where \Omega is a bounded domain with smooth boundary (or, \Omega is a strictly convex, bounded smooth domain in \mathbb R^N) in \mathbb R^N with N\geq 2, f satisfies a new structure condition at infinity, b \in C^\alpha_{\rm loc}({\Omega}) for some \alpha\in (0, 1) which is nonnegative nontrivial in \Omega, but may be vanishing or singular on \partial \Omega,  and A(u) is the Laplacian operator; the p-Laplacian operator; the infinity Laplacian and the Monge-Amp\`{e}re operator, respectively.

 

(21)张志涛   中国科学院

题目Some new results on Henon-Lane-Emden conjecture and Schrodinger systems

摘要We prove Henon-Lane-Emden conjecture is true for space dimension . We prove some new results on some Schrodinger systems: symmetry and asymptotic behavior of ground state solutions; bifurcation and multiple existence of positive solutions; uniqueness and structure of positive solutions; symmetry breaking via Morse index; limit configurations of Schrodinger systems versus  optimal partition for the principal eigenvalue of elliptic systems. We also give Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on .

 

(22)邹文明清华大学

B

 

 

 

 

 

 

 

 

 

 

 

交通信息

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乘坐出租约26元。

(2)大连站大连星海高尔夫酒店:

地铁:(3元)步行640米,到达友好广场站(D口),乘坐地铁2号线,往机场方向乘车5站,约12分钟,到西安路站下车,站内换乘地铁1号线,往河口方向乘车2站,约5分钟,到会展中心站(A口),步行590米,到达终点(高尔夫商务酒店)。

公交:(1元)步行500米到友好广场站,乘坐16/23/901路,往大连海洋大学方向乘车8站,约25分钟,到达会展中心站,步行730米,到达终点(高尔夫商务酒店)。

乘坐出租约16元。

(3)  大连北站大连星海高尔夫酒店:

地铁:(4元)步行280米,到大连北站(A2口),乘坐地铁1号线,往河口方向乘车13站,约31分钟,到会展中心站(A口),步行590米,到达终点(高尔夫商务酒店)。

乘坐出租约38元。

大连星海高尔夫酒店位置图

         

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