姓   名：吴元泽

职   称：教授

人才称号：云南省杰出青年基金获得者

世界华人数学家联盟大会（ICCM）45分钟报告人

工作单位：云南师范大学数学学院 基础数学系

电子邮箱：yuanze.wu@ynnu.edu.cn

研究方向及招生情况

  研究领域：偏微分方程、几何分析

  招生专业：偏微分方程（博士、硕士）、几何分析（博士、硕士）

教育经历

  2008.09——2013.06，苏州大学，基础数学，博士

  2004.09——2008.06，苏州大学，数学与应用数学（师范），本科

获奖情况

 2022 江苏省数学成就奖

学术兼职

 中国数学会会员、美国《数学评论》评论员

科研项目

2027.01--2031.12，Brezıs-Nirenberg方程变号解的爆破分析，国家自然科学基金重点项目“约化方法在若干椭圆及抛物方程中的应用”（批准号12631008）课题，主持

2027.01--2031.12，Brezis-Nirenberg方程变号解非典型集中现象的研究(批准号12671144)，国家自然科学基金面上项目，主持

2026.6--2028.5，非线性泛函分析及其在变分型椭圆方程中的应用（批准号 202601CJ070001），云南省基础研究专项-青年项目（A类），主持

2022.01--2025.12，几类混合型多重耦合椭圆方程组的研究(批准号12171470)，国家自然科学基金面上项目，主持

2018.01--2020.12，关于一类含临界Sobolev指数的Kirchhoff方程的研究(批准号11701554)，国家自然科学基金青年项目，主持

2017.01--2012.12，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(批准号11626226)，国家自然科学基金数学天元青年项目，主持

2020.01--2023.12，几类非线性椭圆方程和椭圆系统研究(批准号11971339)，国家自然科学基金面上项目，参与

2019.01--2022.12，变分包含以及最优控制的研究(批准号11771319)，国家自然科学基金面上项目，参与

专    作

[1] 刘娜，吴元泽，Nehari流形方法及其在椭圆方程组中的应用，中国矿业大学出版社，2026.

论 文

代表性论文：

[1] Juncheng Wei, Yuanze Wu, Stability of the Caffarelli–Kohn–Nirenberg inequality along the Felli–Schneider curve: Critical points at infinity, Proceedings of the London

Mathematical Society, 132(2026), e70146.

[2] Juncheng Wei, Yuanze Wu, On the stability of the Caffarelli-Kohn-Nirenberg inequality, Mathematische Annalen, 384(2022), 1509–1546.

[3]  Juncheng Wei, Yuanze Wu, Ground states of nonlinear elliptic systems with mixed couplings, Journal de Mathématiques Pures et Appliquées, 141(2020), 50–88.

[4]  Juncheng Wei, Yuanze Wu,  Normalized solutions for Schrodinger equations with critical Sobolev exponent and mixed nonlinearities, Journal of Functional Analysis, 283(2022), article 109574.

[5] Fengliu Li, Giusi Vaira, Juncheng Wei, Yuanze Wu, Construction of bubbling solutions of the Brezis-Nirenberg problem in general bounded domains (I): the dimensions 4 and 5, Journal of the London Mathematical Society, 112(2025), Paper No. e70246.

近五年其他论文：

[1] Tuoxin Li, Juncheng Wei, Yuanze Wu, Infinitely many nonradial positive solutions for multi-species nonlinear Schrodinger systems in RN, Journal of Differential Equations, 381(2024), 340–396.

[2] Juncheng Wei, Yuanze Wu, Stability of the Caffarelli-Kohn-Nirenberg inequality: Existence of minimizers, Mathematische Zeitschrift, 308(2024), article 64.

[3] Chao Ji, Zhi-Qiang Wang, Yuanze Wu, A monotone property of the ground state energy to the scalarfield equation and applications, Journal of the London Mathematical Society, 100(2019), 804–824.

[4] 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.

[5] Juncheng Wei, Yuanze Wu, On some Schrodinger equations in RN, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153(2023), 1503–1528.

[6] Fengliu Li, Giusi Vaira, Juncheng Wei, Yuanze Wu, On Brezis-Nirenberg problems: open questions and new results in dimension six, Discrete and Continuous Dynamical Systems, 54(2026), 151–176.

[7] Taicheng Liu, Yuanze Wu, Extremal values of L2-Pohozaev manifolds and their applications, Discrete and Continuous Dynamical Systems, 53(2026), 30–53.

[8] Zhiguo Wu, Yuanze Wu, Positive ground state solutions of the critical nonlinear Schrodinger system with the harmonic potentials for the cooperative case, Topological Methods in Nonlinear Analysis, 66(2025), 755–782.

[9] Zhiguo Wu, Yuanze Wu, Positive ground state solutions of the two coupled nonlinear Schrodinger system with the harmonic potential and the energy critical nonlinearities, Communications on Pure and Applied Analysis, 24(2025), 1000–1018.

[10] Yuanze Wu, Zhi-Qiang Wang, Global behavior of the ground state energy of the nonlinear scalar field equation, Scientia Sinica Mathematics, 53(2023), 25–40. (In chinese)

预印本论文：

[1] Rui He, Xiangqing Liu, Juncheng Wei, Yuanze Wu, A refined blow-up analysis of the Brezis-Nirenberg equation and its application: The one-bubble case for N ≥ 4, arXiv, 2026.

[2] Xinfu Li, Xiangqing Liu, Yuanze Wu, Juncheng Wei, Existence and multiplicity of solutions to the mean-field games model with mixed interactions, arXiv, 2026.

[3] Fengliu Li, Giusi Vaira, Juncheng Wei, Yuanze Wu, Construction of bubbling solutions of the 3d Brezis-Nirenberg problem in general bounded domains, preprint, 2026.

[4] Na Liu, Xiangqing Liu, Yuanze Wu, Reqularity of the ground state energy of the fractional Schrodinger equation and its applications, preprint, 2026.

[5] Yuanze Wu, Zhiguo Wu, Multiple normalized solutions for Brezis-Nirenberg type system with the harmonic potential, preprint, 2026.