吴元泽，男，汉族，江苏苏州人，1985年3月生，共产党员。现任中国矿业大学数学学院教授、博士生导师、数学系科研副主任，兼任第十三届江苏省数学会理事、美国数学会《Mathmatical Reviews》评论员。获第八届江苏省数学成就奖，主持国家自然科学基金面上项目、青年基金、数学天元基金等纵向项目8项，在Math. Ann., J. Math. Pures Appl., J. Funct. Anal., Nonlinearity, Calc. Var. PDEs, J. Differential Equations, J. London Math. Soc.等国际权威期刊发表论文多篇，入选中国矿业大学青年学术带头人、优秀青年骨干教师培养计划。

 

一、教育经历

1.  2008/09 - 2013/06，苏州大学，数学科学学院，基础数学专业，理学博士（导师黄毅生教授）

2. 2004/09 - 2008/06，苏州大学，数学科学学院，数学与应用数学（师范）专业，理学学士

 

二、工作经历

1. 2024.1-至今，中国矿业大学，数学学院，教授
   

2. 2023.1-2023.12，中国矿业大学，数学学院，教授（预聘）

3. 2018/01 -2022/12，中国矿业大学，数学学院，副教授

4. 2013/07 - 2017/12，中国矿业大学，数学学院，讲师

5. 2018/10-2019/09，加拿大不列颠哥伦比亚大学（University of British Columbia），数学系，访问学者，合作导师：魏军城(Juncheng Wei)教授（加拿大皇家科学院院士）

6. 2014/09-2014/09，台湾公立高雄大学，应用数学系，访问学者，合作导师：吴宗芳(Tsung-Fang Wu)教授

7. 2014/07-2014/08，清华大学，数学科学系，访问学者，合作导师：邹文明(Wenming Zou)教授（国家杰出青年基金获得者）

 

三、教学简介：

江苏省一流课程《数学分析》主讲教师之一。主持校级青年教改项目1项，参加校级教改项目2项。获校级教学竞赛一等奖1项、省级教学竞赛三等奖1项，获校级教学成果一等奖1项、其他校级奖励2项。

 

近三年授课信息：

2022-2023-1  数学分析1、数学分析3

2022-2023-2  数学分析2

2023-2024-1 数学分析3、广义函数与索比列夫空间（研究生）、现代偏微分方程理论及应用（研究生）

2023-2024-2 数学分析2

2024-2025-1 数学分析3、广义函数与索比列夫空间（研究生）

 

四、科研简介：

从事非线性泛函分析和非线性椭圆方程（组）的研究工作。目前的兴趣为几何与泛函不等式的稳定性、非线性薛定谔方程预定质量解的存在性和多重性、与玻色-爱因斯坦凝聚相关的非线性椭圆方程（组）非平凡解的存在性和多重性等。获第八届江苏省数学成就奖，入选中国矿业大学第十批青年学术带头人、第十批优秀青年骨干教师，获评2020-2021学年科研育人先进个人。

 

4.1 科研项目：

1. 几类混合型多重耦合椭圆方程组的研究，12171470，国家自然科学基金面上项目，2022-01至2025-12，51万，主持

2. 关于一类含临界Sobolev指数的Kirchhoff方程的研究，11701554，国家自然科学基金青年项目, 2018-01至2020-12，22万，主持

3. 关于全空间上一类Kirchhoff型方程正解的存在性和多重性的研究，11626226，国家自然科学基金天元项目，2017-01至2017-12，3万，主持

4. 关于两类Kirchhoff型方程的研究，2017XKQY091，中央高校基本科研业务费，2017-01至2019-12，20万，主持

5. 含变号位势的非线性薛定谔方程解的研究，2014QNA67，中央高校基本科研业务费，2014-01至2016-12，10万，主持

 

4.2 发表论文：

4.2.1 泛函不等式的稳定性

1. Juncheng Wei, Yuanze Wu, Stability of the Caffarelli-Kohn-Nirenberg inequality: Existence of minimizers, Math. Z., (308)2024, article 64.

2. Juncheng Wei, Yuanze Wu, Sharp stability of the logarithmic Sobolev inequality in the critical point setting, Advances in Analysis and Geometry, Potentials and Partial Differential Equations-The Legacy of David R. Adams, 8(2023), 77-102.

3. Juncheng Wei, Yuanze Wu,  On the stability of the Caffarelli-Kohn-Nirenberg inequality, Math. Ann., 384(2022), 1509-1546.

4.2.2 玻色-爱因斯坦凝聚方程（组）

1. Tuoxin Li, Juncheng Wei, Yuanze Wu, Infinitely many nonradial positive solutions for multi-species nonlinear Schrödinger systems in RN, J. Differential Equations, 381(2024), 340-396.

2. 吴元泽, 王志强, 非线性数量场方程基态能量的整体性态, 中国科学: 数学, 53(2023), 25-40.

3. Juncheng Wei, Yuanze Wu, Ground states of nonlinear elliptic systems with mixed couplings, J. Math. Pures Appl., 141(2020), 50-88.

4. Chao Ji, Zhi-Qiang Wang, Yuanze Wu, A monotone property of the ground state energy to the scalarfield equation and applications, J. London Math. Soc., 100(2019), 804-824.

5. Yuanze Wu, Tsung-Fang Wu, Wenming Zou, On a two-component Bose–Einstein condensate with steep potential wells, Ann. Mat. Pura Appl., 196(2017), 1695-1737.

6. Juntao Sun, Tsung-fang Wu, Yuanze Wu, Existence of nontrivial solution for Schrodinger–Poisson systems with indefinite steep potential well, Z. Angew. Math. Phys., 68(2017), article 73.

7. Yisheng Huang, Zeng Liu, Yuanze Wu, On a biharmonic equation with steep potential and indefinite potential, Adv. Nonlinear Stud., 16(2016),699-717.

8. Yuanze Wu, Yisheng Huang, Zeng Liu, Kirchhoff type problem with potential well and indefinite potential, Electron. J. Differential Equations, 2016(2016), article 178.

9. Yuanze Wu, Yisheng Huang, Zeng Liu, On a Kirchhoff type problem in RN, J. Math. Anal. Appl., 425(2015), 548-564.

10. Yisheng Huang, Tsung-fang Wu, Yuanze Wu, Multiple positive solutions for a class of concave–convex elliptic problems in RN involving sign-changing weight, II, Commun. Contemp. Math., 17(2015), article 1450045.

11. Yuanze Wu, Yisheng Huang, Zeng Liu, Sign-changing solutions for Schrodinger equations with vanishing and sign-changing potentials, Acta Math. Sci. Ser. B (Engl. Ed.), 34(2014), 691-702.

12. Yisheng Huang, Zeng Liu, Yuanze Wu, On a nonlinear Schrodinger equation with indefinite potential, Nonlinear Anal. Real World Appl., 17(2014), 161-170.

13. Yuanze Wu, Yisheng Huang, Sign-changing solutions for Schrodinger equations with indefinite supperlinear nonlinearities, J. Math. Anal. Appl., 401(2013), 850-860.

14. Yisheng Huang, Zeng Liu, Yuanze Wu,  Existence of prescribed L2-norm solutions for a class of Schrodinger-Poisson equation, Abstr. Appl. Anal., 2013(2013), article 398164.

4.2.3 临界椭圆方程（组）

1. Dmitry E. Pelinovsky, Juncheng Wei, Yuanze Wu, Positive solutions of the Gross-Pitaevskii equation for energy critical and supercritical nonlinearities, Nonlinearity, 36(2023), 3684-3709.

2. Juncheng Wei, Yuanze Wu, On some Schrodinger equations in RN, Proc. Roy. Soc. Edinburgh Sect. A, 153(2023), 1503-1528.

3. Juncheng Wei, Yuanze Wu,  Normalized solutions for Schrodinger equations with critical Sobolev exponent and mixed nonlinearities, J. Funct. Anal., 283(2022), article 109574.

4. Yuanze Wu, Wenming Zou, On a critical Schrödinger system in R4 with steep potential wells, Nonlinear Anal., 191(2020), article 111643.

5. Yuanze Wu, Wenming Zou, Spikes of the two-component elliptic system in R4 with thecritical Sobolev exponent, Calc. Var., 58(2019), article 24.

6. Yuanze Wu, Ground state of a K-component critical system with linear and nonlinear couplings: an attractive case, Adv. Nonlinear Stud., 19(2019), 595-623.

7. Yuanze Wu, On finding the ground state solution to the linearly coupled Brezis-Nirenberg system in high dimensions: the cooperative case, Topol. Methods Nonlinear Anal., 53(2019), 697-729.

8. Yuanze Wu, Spikes of sign-changing solutions to the critical Schrodinger equations with trapping potentials, Appl. Anal., 98(2019), 1027-1041.

9. Yuanze Wu, On the semiclassical solutions of a two-component elliptic system in R4 with trapping potentials and Sobolev critical exponent: the repulsive case, Z. Angew. Math. Phys., 69(2018), article 111.

10. Yuanze Wu, Least energy sign-changing solutions of the singularly perturbed Brezis-Nirenberg problem, Nonlinear Anal., 171(2018), 85-101.

11. Yuanze Wu, Sign-changing semi-classical solutions of the Brezis-Nirenberg problems with jump nonlinearities in high dimensions, J. Math. Anal. Appl., 461(2018), 7-23.

12. Yisheng Huang, Zeng Liu, Yuanze Wu, On Kirchhoff type equations with critical Sobolev exponent, J. Math. Anal. Appl., 462(2018), 483-504.

13. Yuanze Wu, On a K-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case, Calc. Var., 56(2017), article 151.

14. 吴元泽, 吴宗芳, 刘增, 关于含非齐次Dirichlet边值的Brezis-Nirenberg问题的研究, 数学物理学报, 35(2015), 1025-1043.

4.2.4 其他椭圆方程（组）

1. Juncheng Wei, Yuanze Wu,  Infinitely many vortex solutions of the magnetic Ginzburg-Landau equation with external potentials in R^2, J. Math. Phys., 62(2021), 041509, 33 pp.

2. Juncheng Wei, Yuanze Wu,  Local uniqueness of the magnetic Ginzburg-Landau equation, J. Elliptic Parabol. Equ., 6(2020), 187-209. (Special Issue for Celebration of the 70th Birthday of Professor Michel Chipot)

3. Yisheng Huang, Yuanze Wu, On a Kirchhoff Equation in Bounded Domains, Adv. Nonlinear Stud., 18(2018), 613-648.

4. Yisheng Huang, Zeng Liu, Yuanze Wu, On finding solutions of a Kirchhoff type problem, Proc. Amer. Math. Soc., 144(2016), 3019-3033.

5. Yuanze Wu, Yisheng Huang, Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent, Bound. Value Probl., 2013(2013), article 149.

 

4.3 预印本论文：

1. Juncheng Wei, Yuanze Wu, Stability of  the Caffarelli-Kohn-Nirenberg inequality along the Felli-Schneider curve: critical points at infinity, preprint, 2024.
   

五、指导学生

博士生：2023级：李枫柳，2022级：吴志国

硕士生：2024级：李舒娅、沈文桓，2023级：王兆年、吴庚鑫，2022级：李小璐、刘泰成

已毕业学生：邢相斌（2020级硕士）

六、联系方式

Email: wuyz850306@cumt.edu.cn

通讯地址：江苏省徐州市中国矿业大学南湖校区数学学院B309

邮政编码：221116