向长林个人简介

一、基本信息

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

（1）2017年指导本科生毕业论文， 4人；

（2）2019年指导本科生毕业论文：4人；

（3）2020年指导本科生毕业论文：5人；研究生毕业论文（第二导师）：1人

3. 主持及参与的教学研究项目

无

四、近几年的学术研究

1、承担的学术研究课题

（1）Kirchhoff方程奇异摄动问题的研究（11701045），国家自然科学青年基金项目，2018.01

～2020.12，主持人

2、发表的学术论文

（1）Partial regularity of solutions to a linear elliptic system with quadratic Jacobian stru

cture. 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. Edinbur

gh Sect. A 149 (2019), 1097-1122. (with Peng Luo, Shuangjie Peng, Chunhua Wang).

（7）Some regularity results for p-harmonic mappings between Riemannian manifolds. Non

linear 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 grow

th. 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, 22

07-2218.

（12）Gradient estimates for solutions to quasilinear elliptic equations with critical Sobolev gr

owth 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 dimen

sions. Calc. Val. Partial Differential Equations 55 (2016), 55:134.

（14）Remarks on nondegeneracy of ground states for quasilinear Schrodinger equations. Di

screte Contin. Dyn. Syst. 36 (2016), 5789-5800.

（15）Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic eq

uations. 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 b

oundary geometry. Ann. Acad. Sci. Fenn. Math. 41 (2016), 973-1004. (with Chunhua Wa

ng).

（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）L^∞-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.