Zhong Xuexiu
Field: ;Elliptic and parabolic partial differential equations ;Functional Analysis; Variational method and critical point theory
zhongxuexiu1989@163.com & 20190117@m.scnu.edu.cn

Education

Aug 2009-Jul 2015  Department of Mathematical Sciences, Tsinghua University, PhD Supervisor: Prof. Zou Wenming

Sept 2005-Jul 2009   Department of mathematics and applied mathematics, School of science, South China University of Technology, Bachelor of Science

Experience

2019/05-now : associate researcher, South China Research Center for Applied Mathematics and Interdisciplinary Studies,South China Normal University.
2017 / 07-2019 / 05:  associate researcher, School of mathematics, Sun Yat-sen University.

2015/08-2017/07: postdoctor, Taida Institute for Mathematical Sciences, National Taiwan University,  Co tutor: Professor  Changshou Lin.

Teaching

Graduate courses:
2020-2021 First Semester: Sobolev Space and L2 Theory in Partial Differential Equations
2021-2022 First Semester: Sobolev Space and L2 Theory in Partial Differential Equations
2023-2024 First Semester: Critical Point Theory and Its Applications
2023-2024 First Semester: Elliptic Partial Differential Equations
Undergraduate courses:
2019-2020 First Semester: Advanced Mathematics (I-1)
2020-2021 First Semester: Advanced Mathematics (II)

Academics

【1】 Guangzhou Science and Technology Plan Project, Basic and Applied Basic Research Project (Excellent Doctoral "Endurance" Project), 2024A04J10001, Research on Normative Solution of Nonlinear Schrödinger Equation with Exponential Critical Growth, 2024-01 to 2025-12, 100000 yuan, under research, host
【2】 National Natural Science Foundation of China, General Project, 12271184, Topological Methods for the Study of Normal Solutions to Nonlinear Schrödinger Equations, 2023-01-01 to 2026-12-31,450000 yuan, under research, host
【3】 Guangzhou Science and Technology Plan Project, Basic and Applied Basic Research Project (Doctoral Young Science and Technology Personnel Category), 202102020225, Research on Some Open Issues in Bose Einstein Condensed Systems, 2021-04 to 2023-03, 50000 yuan, completed, host
【4】 Guangdong Provincial Natural Science Foundation, General Project, 2021A1515010034, Research on Solutions to Fixed Mass Problems of Nonlinear Schrödinger Equations with Potential, 2021-01-01 to 2023-12-31, 100000 yuan, completed, host
【5】 Guangdong Provincial Basic and Applied Basic Research Fund Project, Guangdong Hong Kong Macao Applied Mathematics Center Project, 2020B1515310021, Optimal Transmission Modeling and Mathematical Theory of Information Theory, from 2020-01 to 2021-12, 300000 yuan, completed, participation 
【6】 National Natural Science Foundation of China, Youth Science Foundation Project, 11801581, Fractional Caffarelli Kohn Nerenberg Inequality and Its Applications, 2019-01-01 to 2021-12-31, 260000 yuan, completed, host
【7】 Guangdong Provincial Natural Science Foundation, PhD initiated vertical collaboration project, 2018A030310082, non-linear Schrödinger, 2018-05-01 to 2021-04-30, 100000 yuan, completed, host

Honor

Published:
[1] Zhong, Xuexiu; Zou, Wenming. Existence of infinitely many solutions for sublinear elliptic problems. Glasg. Math. J. 54 (2012), no. 3, 535–545.

[2] Zhong, Xuexiu; Zou, Wenming. Ground state and multiple solutions via generalized Nehari manifold. Nonlinear Anal. 102 (2014), 251–263.

[3] Zhong, Xuexiu;  Zou, Wenming. A concentration behavior for semilinear elliptic systems with indefinite weight. Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 12, 2014–2026.

[4] Zhong, Xuexiu;  Zou, Wenming. Critical Schrödinger systems in RN with indefinite weight and Hardy potential. Differential Integral Equations 28 (2015), no. 1-2, 119–154.

[5] 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 54 (2015), no. 2, 1793–1829. (representative work)

[6] Zhong, Xuexiu;  Zou, Wenming. A perturbed nonlinear elliptic PDE with two Hardy-Sobolev critical exponents. Commun. Contemp. Math. 18 (2016), no. 4, 1550061, 26 pp.

[7] Lin, Chang-Shou; Yang, Wen; Zhong, Xuexiu A priori estimates of Toda systems, I: the Lie algebras of An, Bn, Cn and G2. J. Differential Geom. 114 (2020), no. 2, 337–391. (representative work)

[8] Zhong, Xuexiu;  Zou, Wenming. A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in RN. J. Differential Equations 292 (2021), 354–387. (representative work)

[9] Bartsch, Thomas; Zhong, Xuexiu; Zou, Wenming. Normalized solutions for a coupled Schrödinger system. Math. Ann. 380 (2021), no. 3-4, 1713–1740. (representative work)

[10] Ding, Yanheng; Zhong, Xuexiu Normalized solution to the Schrödinger equation with potential and general nonlinear term: mass super-critical case. J. Differential Equations 334 (2022), 194–215. (representative work)

[11] Wei, Juncheng; Zhong, Xuexiu; Zou, Wenming On Sirakov's open problem and related topics. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 23 (2022), no. 2, 959–992. (representative work)

[12] Guo,Zhenyu; Zhong, Xuexiu. On a fractional Hardy-Sobolev inequality with two variables. Rocky Mountain Journal of Mathematics, 52 (2022), no. 5, 1643-1660.
 
[13] 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 Integral Equations 36 (2023), no. 1-2, 133–160.
 
[14] Deng, Yinbin; Shuai Wei; Zhong, Xuexiu. Existence and Concentration Result for the General Kirchhoff Type Equations. J. Geom. Anal. 33(2023), no.3, Paper No. 88, 22 pp. 
 
[15] He, Qihan; Lv, Zongyan; Zhang, Yimin; Zhong, Xuexiu. Existence and blow up behavior of  positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical. J. Differential Equations. (representative work)
 
[16] Deng, Yinbin; He, Qihan; Pan, Yiqing; Zhong, Xuexiu. The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation, Adv. Nonlinear Stud. 23(2023), no. 1, Paper No. 20220049, 22 pp.
 
[17] Zhang, Jianjun; Zhong, Xuexiu; Zhou, Huansong. Bifurcation from the essential spectrum for an elliptic equation with general nonlinearities. Sci. China Math. 66(2023), no. 10, 2243-2260. (representative work)
 
[18] Zeng, Xiaoyu; Zhang, Jianjun; Zhang, Yimin; Zhong, Xuexiu. On the Kirchhoff equation with prescribed mass and general nonlinearities. Discrete Contin. Dyn. Syst. Ser. S 16(2023), no.11, 3394-3409.
 
[19] Huang, Chen; Zhang, Jianjun; Zhong, Xuexiu. Existence and multiplicity of solutions for general quasi-linear elliptic equations with sub-cubic nonlinearities. J. Math. Anal. Appl. 531(2024), no. 1, Paper No. 127880, 25 pp.
 
[20] Jeanjean, Louis; Zhang, Jianjun; Zhong, Xuexiu. A global branch approach to normalized solutions for the Schrödinger equation. J. Math. Pures. Appl.(9) 183(2024), 44-75. (representative work)

[21] Kang, Yuting; Luo, Peng; Xiang, Chang-Lin; Zhong, Xuexiu. Uniqueness and nondegeneracy of positive solutions of general Kirchhoff Type Equations. Acta Mathematicae Applicatae Sinica, to appear

[22] Liu, Wenmin; Zhong, Xuexiu; Zhou, Jinfang. Normalized solutions for the General Kirchhoff Type Equations. Acta Math. Sci. Ser. B (Engl. Ed.), to appear

[23] Jeanjean, Louis; Zhang, Jianjun; Zhong, Xuexiu. Normalized ground states for a coupled Schrödinger system: Mass super-critical case. NoDEA Nonlinear Differential Equations Appl. to appear
 

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)






 

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