研究生课程：
2020--2021学年第1学期：Sobolev 空间与偏微分方程的 L^2 理论
2021-2022学年第1学期：Sobolev 空间与偏微分方程的 L^2 理论
2023-2024学年第1学期： 临界点理论及其应用
2023-2024学年第1学期： 椭圆型偏微分方程
2024春：线性偏微分方程L2理论和Sobolev空间

本科生课程：
2019-2020学年第1学期： 高等数学（I-1）
2020-2021学年第1学期：高等数学（II）

【1】广州市科技计划项目，基础与应用基础研究项目（优秀博士“续航”项目），2024A04J10001，带指数临界增长的非线性薛定谔方程规范化解的研究，2024-01 至 2025-12，10万元，在研，主持
【2】国家自然科学基金委员会，面上项目，12271184，非线性薛定谔方程正规化解研究的拓扑方法，2023-01-01 至 2026-12-31,45万元，在研，主持
【3】广州市科技计划项目，基础与应用基础研究项目（博士青年科技人员类），202102020225，玻色-爱恩斯坦凝聚系统中的一些公开问题的研究，2021-04 至 2023-03,5万元，结题，主持
【4】广东省自然科学基金，面上项目，2021A1515010034,带位势的非线性薛定谔方程固定质量问题解的研究, 2021-01-01 至 2023-12-31，10万元，准备结题，主持
【5】广东省基础与应用基础研究基金项目，粤港澳应用数学中心项目，2020B1515310021，信息论的最优传输建模和数学理论，2020-01 至 2021-12， 30万元，参与
【6】国家自然科学基金委员会，青年科学基金项目，11801581，分数阶Caffarelli-Kohn-Nirenberg不等式及其应用，2019-01-01 至 2021-12-31，结题，主持
【7】广东省自然科学基金，博士启动纵向协同项目，2018A030310082,非线性Schrödinger, 2018-05-01 至 2021-04-30，10万元，结题，主持

                                                                                 2024年
1. Deng, Shengbing, Huang, Ling, Zhang, Jianjun, Zhong, Xuexiu*. Normalized solutions for a coupled Schrödinger systems in R2 with exponential critical growth: Mass super-critical case. Journal of Differential Equations,2024, 411: 349-380  (代表作)
2. Huang, Ling, Wen, Hangxin, Zhang, Jianjun*, Zhong, Xuexiu. Normalized solutions for the fractional P -Laplacian equation with exponential critical growth. Complex Variables and Elliptic Equations,Informa UK Limited, 2024  
3. Dou, Jingbo, Huang, Ling, Zhong, Xuexiu*. Normalized Solutions to N-Laplacian Equations in  RN with Exponential Critical Growth. J. Geom. Anal., 2024, 34:317  
4. Liu, Wenmin, Zhong, Xuexiu*, Zhou, Jinfang. Normalized solutions for the general Kirchhoff type equations. Acta Mathematica Scientia,2024, 44(5): 1886–1902  
5. Jeanjean, Louis*, Zhang, Jianjun, Zhong, Xuexiu. Normalized ground states for a coupled Schrödinger system: mass super-critical case. Nonlinear Differential Equations and Applications NoDEA, 2024, 31:85  
6. Jeanjean, Louis*, Zhang, Jianjun, Zhong, Xuexiu. A global branch approach to normalized solutions for the Schr\"odinger equation. J. Math. Pures Appl. (9),2024, 183: 44--75  （代表作）
7. Huang, Chen, Zhang, Jianjun*, Zhong, Xuexiu. Existence and multiplicity of solutions for general quasi-linear elliptic equations with sub-cubic nonlinearities. Journal of Mathematical Analysis and Applications,2024, 531: 127880
                                                                                   2023年 
8. Zeng, Xiaoyu, Zhang, Jianjun, Zhang, Yimin, Zhong, Xuexiu*. On the Kirchhoff equation with prescribed mass and general nonlinearities. Discrete and Continuous Dynamical Systems - S,American Institute of Mathematical Sciences (AIMS), 2023, 16(11): 3394–3409  
9. Zhong, Xuexiu*, Zou, Wenming. A new deduction of the strict sub-additive inequality and its application: Ground state normalized solution to Schrödinger equations with potential. Differential and Integral Equations,2023, 36(1/2): 133-160  
10. Zhang, Jianjun, Zhong, Xuexiu, Zhou, Huansong*. Bifurcation from the essential spectrum for an elliptic equation with general nonlinearities. Sci. China Math.,2023, 66(10): 2243--2260  （代表作）
11. He, Qihan, Lv, Zongyan, Zhang, Yimin, Zhong, Xuexiu*. Existence and blow up behavior of positive normalized solution to the Kirchhoff equation with general nonlinearities: mass super-critical case. J. Differential Equations,2023, 356: 375--406  （代表作）
12. Deng, Yinbin, Shuai, Wei, Zhong, Xuexiu*. Existence and concentration results for the general Kirchhoff-type equations. J. Geom. Anal.,2023, 33(3): Paper No. 88, 22  
13. Deng, Yinbin, He, Qihan*, Pan, Yiqing, Zhong, Xuexiu. The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation. Advanced Nonlinear Studies,2023, 23: 20220049  
                                                                                  2022年
14. Ding, Yanheng, Zhong, Xuexiu*. Normalized solution to the Schr\"odinger equation with potential and general nonlinear term: mass super-critical case. J. Differential Equations,2022, 334: 194--215  （代表作）
15. Wei, Juncheng*, Zhong, Xuexiu, Zou, Wenming. On Sirakov's open problem and related topics. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5),2022, 23(2): 959--992  （代表作）
16. Guo, Zhenyu*, Zhong, Xuexiu. On a fractional Hardy–Sobolev inequality with two-variables. Rocky Mountain Journal of Mathematics,2022, 52(5): 1643-1660  
                                                                                   2021年
17. Bartsch, Thomas, Zhong, Xuexiu*, Zou, Wenming. Normalized solutions for a coupled Schr\"odinger system. Math. Ann.,2021, 380(3-4): 1713--1740  （高被引热点论文，代表作）
18. Zhong, Xuexiu*, Zou, Wenming. A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in RN. J. Differential Equations,2021, 292: 354--387  （代表作）
                                                                                   2020年
19. Lin, Chang-Shou*, Yang, Wen, Zhong, Xuexiu. A Priori estimates of Toda systems, I: the Lie algebras of $A_n,B_n,C_n$ and $G_2$. J. Differential Geom.,2020, 114(2): 337--391  （代表作）
                                                                                   2016年
20. Zhong, Xuexiu*, Zou, Wenming. A perturbed nonlinear elliptic PDE with two Hardy–Sobolev critical exponents. Communications in Contemporary Mathematics, 2016, 18(04): 1550061, 26 pp.  
                                                                                  2015年
21. Zhong, Xuexiu*, Zou, Wenming. Critical Schrödinger systems in $mathbb R^N$ with indefinite weight and Hardy potential. Differential and Integral Equations, 2015, 28(1/2): 119–154.  
22. Cerami, Giovanna, Zhong, Xuexiu, Zou, Wenming*. On some nonlinear elliptic PDEs with Sobolev-Hardy critical exponents and a Li-Lin open problem. Calc. Var. Partial Differential Equations,2015, 54(2): 1793--1829  （代表作）
                                                                                   2014年
23. Zhong, Xuexiu*, Zou, Wenming. A concentration behavior for semilinear elliptic systems with indefinite weight. Acta Mathematica Sinica, English Series, 2014, 30(12) :2014–2026.  
24. Zhong, Xuexiu*, Zou, Wenming. Ground state and multiple solutions via generalized Nehari manifold. Nonlinear Analysis: Theory, Methods & Applications,2014, 102: 251–263.  
                                                                                  2012年
25. ZHONG, X., ZOU, W.*. EXISTENCE OF INFINITELY MANY SOLUTIONS FOR SUBLINEAR ELLIPTIC PROBLEMS. Glasgow Mathematical Journal,2012, 54(3): 535–545.
其他相关个人主页：
https://www.researchgate.net/profile/Zhong_Xuexiu

钟学秀，华南师范大学 华南数学应用与交叉研究中心/数学科学学院 (scholat.com)

 

近年来的学术活动：
\item[1.] {\bf 钟学秀}; BEC系统中有关最佳常数的计算, 非线性泛函分析及其前沿进展青年学术研讨会, 广东广州--华南理工大学,2020/01/03 ---- 2020/01/05 \textcolor{red}{(会议报告)}

\item[2.]{\bf 钟学秀}; Ground state normalized solution to the Schr\"odinger  equation with potential, 中国矿业大学,2020/11/16 \textcolor{red}{(邀请报告)}

\item[3.] {\bf 钟学秀}; 带位势的非线性薛定谔方程的规范基态解,武汉理工大学,2020/12/04\textcolor{red}{(邀请报告)}

\item[4.] {\bf 钟学秀}; 非线性薛定谔方程和系统规范正解的研究, 2021年西安PDE和几何分析青年学者研讨会,陕西西安, 2021/07/20 ---- 2021/07/22 \textcolor{red}{(会议报告)}

\item[5.]{\bf 钟学秀};带位势和一般非线性项的薛定谔系统的规范基态解,非线性分析国际会议暨第二十一届全国非线性泛函分析会议,云南昆明,2021/07/23----2021/07/26  \textcolor{red}{(国际会议分组报告)}

\item[6.]{\bf 钟学秀};On the positive normalized solution to the Sch\"odinger equation with general nonlinearities,华中师范大学,2021/10/18\textcolor{red}{(邀请报告)}

\item[7.] {\bf 钟学秀}; Positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical, 浙江师范大学,2021/10/20,\textcolor{red}{(邀请报告)}

\item[8.]{\bf 钟学秀}; Positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical, 北京航空航天大学,2021/10/21 \textcolor{red}{(邀请报告)}

\item[9.] {\bf 钟学秀}; On the positive normalized solution to the Sch\"odinger equation with general nonlinearities,中国地质大学,2021/10/24\textcolor{red}{(邀请报告)}

\item[10.] {\bf 钟学秀}; Positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical,重庆师范大学, 2021/11/01 \textcolor{red}{(邀请报告)}

\item[11.]{\bf 钟学秀};On Stuart's open problem and beyond;规范化解的基本研究方法;规范化解研究的新思想:基于连续性方法;基于连续性方法研究规范化解的最新进展. 重庆交通大学,2021/11/03----2021/11/07  \textcolor{red}{(邀请专题系列讲座报告)}

\item[12.]{\bf 钟学秀};带位势的非线性薛定谔方程的规范基态解,偏微分方程青年论坛,广西大学,2021/11/14----2021/11/15\textcolor{red}{(会议报告)}

\item[13.] {\bf 钟学秀}; Global alternative without eigenvalues and its application on normalized solutions for the  Schr\"odinger equation, 苏州科技大学,2021/11/18,\textcolor{red}{(邀请报告)}

\item[14.]{\bf 钟学秀}; 无特征值的全局选择定理及其在薛定谔方程规范解问题的应用,2021年中山大学偏微分方程与动力系统学术研讨会,深圳, 2021/11/26 至 2021/11/28 \textcolor{red}{(会议 报告)}

\item[15.] {\bf 钟学秀}; 连续性方法在若干椭圆问题的应用,浙江师范大学,2022/04/27\textcolor{red}{(邀请报告)}

\item[16.] {\bf 钟学秀}; 连续性方法在若干椭圆问题的应用,三峡大学, 2022/04/28 \textcolor{red}{(邀请报告)}

\item[17.]{\bf 钟学秀}; 连续性方法在若干椭圆问题的应用,广东工业大学, 2022/05/24 \textcolor{red}{(邀请报告)}

\item[18.]{\bf 钟学秀};Bifurcation from essential spectrum for an elliptic equation with general nonlinearity,非线性泛函分析青年学术论坛,西北工业大学,2022/05/27----2022/05/29\textcolor{red}{(会议报告)}

\item[19.] {\bf 钟学秀}; 连续性方法在若干椭圆问题的应用, 华中师范大学,2022/06/23,\textcolor{red}{(邀请报告)}

\item[20.]{\bf 钟学秀}; 连续性方法在若干椭圆问题的应用, 中国矿业大学,2022/07/02----2022/07/03,\textcolor{red}{(会议报告)}

\item[21.] {\bf 钟学秀}; Uniqueness and nondegeneracy of positive solutions of general Kirchhoff Type Equations,中山大学,2022/09/10\textcolor{red}{(小型学术会议报告)}

\item[22.] {\bf 钟学秀}; Existence and blow up behavior of positive normalized solution to the Kirchhoff equation with general nonlinearities: Mass super-critical case,曲靖师范大学, 2022/09/30 \textcolor{red}{(邀请报告)}

\item[23.]{\bf 钟学秀}; On the normalized solutions to the Schr\"odinger systems and scalar equations,华南师范大学, 2022/11/04----2022/11/06 \textcolor{red}{(会议报告)}

\item[24.]{\bf 钟学秀};On the normalized solutions to the Schr\"odinger systems and scalar equations,苏州科技大学,2022/11/14\textcolor{red}{(邀请报告)}

\item[25.] {\bf 钟学秀}; On the normalized solutions to the Schr\"odinger systems and scalar equations, 重庆交通大学,2022/11/15,\textcolor{red}{(邀请报告)}

\item[26.]{\bf 钟学秀}; On the normalized solutions to the Schr\"odinger systems and scalar equations, 广州大学,2022/11/23,\textcolor{red}{(邀请报告)}

\item[27.] {\bf 钟学秀}; Normalized solutions for a coupled Schr\"odinger system,汕头大学,2023/03/24 \textcolor{red}{(邀请报告)}

\item[28.] {\bf 钟学秀}; On Bartsch-Jeanjean-Soave’s open problem,椭圆偏微分方程与变分法青年学者论坛,深圳大学, 2023/04/14----2023/04/17 \textcolor{red}{(会议报告)}

\item[29.]{\bf 钟学秀}; On Bartsch-Jeanjean-Soave’s open problem, 华南农业大学,2023/04/17\textcolor{red}{(邀请报告)}

\item[30.]{\bf 钟学秀};Bartsch-Jeanjean-Soave公开问题以及全局分支方法的应用,第十届偏微分方程青年学术论坛,西安,2023/05/12----2023/05/15\textcolor{red}{(全国会议分组报告)}

\item[31.] {\bf 钟学秀}; Bartsch-Jeanjean-Soave公开问题以及全局分支方法的应用, 重庆师范大学,2023/05/19,\textcolor{red}{(邀请报告)}

\item[32.]{\bf 钟学秀}; Normalized solutions for a coupled Schr\"odinger system, 第七届中国系统科学大会,重庆,2023/05/19----2023/05/21,\textcolor{red}{(全国会议分组报告)}

\item[33.]{\bf 钟学秀};On the Bartsch-Jeanjean-Soave’s open problem and a global branch approach to study of the normalized solution problems,RISM Congress Analysis and PDEs, Varese, Italy,2023/05/29----2023/05/31,\textcolor{red}{(国际会议特邀大会报告)}

\item[34.]{\bf 钟学秀};On the Bartsch-Jeanjean-Soave’s open problem and a global branch approach to study of the normalized solution problems,中山大学,2023/06/15\textcolor{red}{(小型会议报告)}

\item[35.]{\bf 钟学秀};On the Bartsch-Jeanjean-Soave’s open problem and a global branch approach to study of the normalized solution problems, \textcolor{red}{has been invited as speaker of the thematic session Recent results in nonlinear PDEs and applications of the event that will be held in Foz do Iguacu, Brazil, from July 17th to 21th, 2023.但因签证问题未能前行参加会议}

\item[36.] {\bf 钟学秀};Normalized solutions for nonlinear Schr\"odinger equations with general nonlinearities and Sobolev critical exponents, 兰州大学,2023/10/17,\textcolor{red}{(邀请报告)}

\item[37.] {\bf 钟学秀};An introduction to the study of normalized solution for the nonlinear Schr\"odinger equations and systems, 非线性椭圆型方程青年学者研讨会,山西,太原理工大学,2023/10/20----2023/10/22,\textcolor{red}{(会议报告)}

\item[38.] {\bf 钟学秀};涉及临界增长的非线性薛定谔方程和系统规范化正解研究的相关进展, 华中师范大学,2023/10/26,\textcolor{red}{(邀请报告)}

\item[39.] {\bf 钟学秀};涉及临界增长的非线性薛定谔方程和系统规范化正解研究的相关进展, 武汉理工大学,2023/10/27,\textcolor{red}{(邀请报告)}

\item[40.] {\bf 钟学秀};An introduction to the study of normalized solution for the nonlinear Schr\"odinger equations and systems,非线性色散方程国际学术研讨会,四川成都,电子科技大学,2023/11/03----2023/11/06,\textcolor{red}{(国际会议报告)}

\item[41.] {\bf 钟学秀};非线性薛定谔方程规范化解研究的全局分支方法, 广州大学,2023/12/12,\textcolor{red}{(邀请报告)}

\item[42.]{\bf 钟学秀};全局分支方法在非线性薛定谔方程规范化正解研究中的应用,中国数学会2023年学术年会,大连,2023/12/22----2023/12/26,\textcolor{red}{(非线性泛函分析卫星会议大会报告)}

\item[43.]{\bf 钟学秀};On Soave's open problems for nonlinear Schr\"odinger equations with general nonlinearities and Sobolev critical exponents,非线性分析及其应用青年学者论坛,浙江金华,2024/01/19---2024/01/22,\textcolor{red}{(全国会议报告)}

\item[44.]{\bf 钟学秀};Infinitely many Sign-changing normalized solutions of competition-diffusion p-Laplacian systems,西南大学,2024/02/01,\textcolor{red}{(邀请报告)}

\item[45.]{\bf 钟学秀};耦合薛定谔系统的规范化正解的研究,非线性分析青年学者论坛,云南昆明,2024/03/22---2024/03/25,\textcolor{red}{(全国会议报告)}

\item[46.]{\bf 钟学秀};Infinitely many Sign-changing normalized solutions of competition-diffusion p-Laplacian systems,非线性泛函分析
及其应用青年学者论坛,安徽合肥,2024/04/25---2024/04/27,\textcolor{red}{(全国会议报告)}

\item[47.]{\bf 钟学秀};A global branch approach to normalized solutions for Schr\"odinger equations, International Conference on Elliptic and Parabolic Problems,Recent developments in Nonlinear Elliptic PDEs, Gaeta, Italy,2024/05/20---2024/05/24,\textcolor{red}{(国际会议分主题特邀报告)}

\item[48.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent, 中西南六省（市）应用数学学术会议, 大理,2024/05/31---2024/06/02,\textcolor{red}{(国际会议分组报告)}

\item[49.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent,Workshop on Nonlinear Functional Analysis and Its Application,Chongqing,China,2024/06/14---2024/06/16,\textcolor{red}{(国际会议邀请报告)}

\item[50.]{\bf 钟学秀};On the study of the normalized solution for the nonlinear Schr\"odinger equations,重庆交通大学,2024/06/18,\textcolor{red}{(邀请报告)}

\item[51.]{\bf 钟学秀};关于临界混合质量薛定谔系统正规化解存在性问题,重庆师范大学,2024/06/18,\textcolor{red}{(邀请报告)}

\item[52.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent,访问河南师范大学并做学术报告,2024/06/20---2024/06/22,\textcolor{red}{(邀请报告)}

\item[53.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent,访问湖南大学并在中南大学做学术报告,2024/06/28---2024/06/30,\textcolor{red}{(邀请报告)}

\item[54.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent,访问中国矿业大学-徐州,2024/06/30---2024/07/01,\textcolor{red}{(邀请报告)}

\item[55.]{\bf 钟学秀};非线性薛定谔方程规范化解研究的方法,“第二届联大数学研究生暑期学校”,2024/07/07---2024/07/14,\textcolor{red}{(受邀给全国研究生上课)}

\item[56.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent, 非线性分析与微分方程进展学术研讨会,东北石油大学,2024/07/14---2024/07/17,\textcolor{red}{(全国会议邀请报告)}

\item[57.]{\bf 钟学秀};On positive normalized solutions to a mass mixed coupled Schr\"odinger system with Sobolev critical exponent,云南省数学会2024年学术年会会议，云南腾冲,2024/07/19---2024/07/22,\textcolor{red}{(全国会议邀请报告)}

\item[58.]{\bf 钟学秀};The mass-mixed case for normalized solutions to NLS equations in dimension two, 非线性泛函分析及其应用学术研讨会,贵州大学,贵阳,2024/07/22---2024/07/26,\textcolor{red}{(全国会议邀请报告)}

\item[59.]{\bf 钟学秀};The mass-mixed case for normalized solutions to NLS equations in dimension two,访问安徽大学参加一个小型学术会议并做报告,安徽大学,合肥,2024/07/26---2024/07/28,\textcolor{red}{(邀请报告)}

\item[60.]{\bf 钟学秀};全局分支方法在非线性薛定谔方程规范化正解研究中的应用, 访问陕西师范大学并做学术报告,2024/07/28---2024/08/03,\textcolor{red}{(邀请报告)}

\item[61.]{\bf 钟学秀};全局分支方法在非线性薛定谔方程规范化正解研究中的应用, 访问西北工业大学并做学术报告,2024/07/31,\textcolor{red}{(邀请报告)}

\item[62.]{\bf 钟学秀};The mass-mixed case for normalized solutions to NLS equations in dimension two,非线性偏微分方程与变分方法会议,太原理工大学,太原, 2024/08/02---2024/08/05,\textcolor{red}{(全国会议邀请报告)}

\item[63.]{\bf 钟学秀}; 全局分支方法在非线性薛定谔方程规范化正解研究中的应用,访问西北民族大学并做学术报告,2024/08/05,\textcolor{red}{(邀请报告)}

\item[64.]{\bf 钟学秀};The mass-mixed case for normalized solutions to NLS equations in dimension two,反应扩散方程理论及其应用学术研讨会,兰州大学,2024/08/06---2024/08/09,\textcolor{red}{(全国会议邀请报告)}