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向长林

一、基本信息

 

 

向长林

最终学历

博士

 

副教授

 

 

博士

电子邮件 

changlin.xiang@yangtzeu.edu.cn 

通信地址 

大壕娱乐,湖北省荆州市南环路1 

邮政编码 

434023 

研究方向 

非线性椭圆型偏微分方程变分法,几何分析

社会职务 

 

二、个人简介

1、学习经历

2010.9-2015.9,芬兰于韦斯屈莱大学数学系,基础数学,博士研究生

2007.9-2010.6,华中师范大学数学系,应用数学硕士研究生

2003.9-2007.6,华中师范大学数学系,本科

2、工作经历

2018.9-2019.7华中师范大学,访问学者

2017.6-2017.7,华中师范大学,访问学者

2017.11-至今,  长江大学数学系,副教授

2016.9-2017.10,长江大学数学系,讲师 

2015.10-2016.8,芬兰于韦斯屈莱大学数学系,博士后

三、近五年的教学情况及成果

1、讲授的主要课程

本科生课程:《数学分析》,《数学物理方程》,《泛函分析》

本学院研究生课程:《现代偏微分方程入门》,《泛函分析》

外学院研究生课程:《数学物理方程》

2、承担的实践性教学任务

12017年指导本科生毕业论文, 4人;

22019年指导本科生毕业论文:4人;

32020年指导本科生毕业论文:5人;研究生毕业论文(第二导师):1

3. 主持及参与的教学研究项目

四、近几年的学术研究

1、承担的学术研究课题

1Kirchhoff方程奇异摄动问题的研究(11701045),国家自然科学青年基金项目,2018.012020.12,主持人

2、发表的学术论文

(1) Partial regularity of solutions to a linear elliptic system with quadratic Jacobian structure. Applied Mathematics Letters 111 (2021) 1-6. (with Chang-Yu Guo)

(2) Regularity of solutions for a fourth-order elliptic system via conservation law. J. London Math. Soc. (2) 101 (2020), 907-922. (with Chang-Yu Guo)

(3) Local uniqueness of multi-peak solutions to a class of Kirchhoff equations. Ann. Acad. Sci. Fenn. Math. 45 (2020), 121-137. (with Gongbao Li, Yahui Niu)

(4) Local uniqueness problem for a nonlinear elliptic equation. Commun. Pure Appl. Anal. 19 (2020), no. 2, 1037-1055. (with Miao Chen, Youyan Wan)

(5) A singularly perturbed Kirchhoff problem revisited. J. Differential Equations 268 (2020), no. 2, 541–589. (with Gongbao Li, Peng Luo, Shuangjie Peng, Chunhua Wang)  

(6) Multi-peak positive solutions to a class of  Kirchhoff equations. Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 1097-1122. (with Peng Luo, Shuangjie Peng, Chunhua Wang)

(7) Some regularity results for p-harmonic mappings between Riemannian manifolds. Nonlinear Analysis 188 (2019), 405-424. (With Chang-Yu Guo)

(8) Regularity of quasi-n-harmonic mappings into NPC spaces. Annali di Matematica 198(2019), 367-380. (With Chang-Yu Guo) 

(9) Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth. Applied Mathematics Letters 86 (2018), 270-275. (With Gongbao Li)

(10) Uniqueness of positive solutions to some nonlinear Neumann problems. J. Math. Anal. Appl., 455 (2017), 1835-1847. (with Youyan Wan)

(11) Nonlinear Liouville problems in a quarter plane.  Int. Math. Res. Not. IMRN 2017,  2207-2218.

(12) Gradient estimates for solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential. Acta Math. Sci. Ser. B Engl. Ed. 37 (2017), 58-68.

(13) Uniqueness and nondegeneracy of ground states for Choquard equations in three dimensions. Calc. Val. Partial Differential Equations 55 (2016), 55:134.

(14) Remarks on nondegeneracy of ground states for quasilinear Schrodinger equations. Discrete Contin. Dyn. Syst. 36 (2016), 5789-5800.

(15) Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations. Ann. Acad. Sci. Fenn. Math. 41 (2016), 143-166. (with Cheng-Jun He)

(16) Infinitely many solutions for p-Laplacian equation involving double critical terms and boundary geometry. Ann. Acad. Sci. Fenn. Math. 41 (2016), 973-1004. (with Chunhua Wang)

(17) A note on asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential. J. Math. Anal. Appl., 441(1) (2016), 211-234. (with Cheng-Jun He)

(18) -variational problems associated to measurable Finsler structures. Nonlinear Anal. 132 (2016), 126-140. (with Chang-Yu Guo and Dachun Yang)

(19) Quantitative properties on the steady states to a Schrodinger-Poisson-Slater system.  Acta Math. Sin. (Engl. Ser.) 31 (2015), 1845-1856.

(20) Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential. J. Differential Equations 259 (2015), 3929-3954.

 

 

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