姓 名：吴元泽
职 称：教授
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：非线性泛函分析、偏微分方程
招生专业：非线性分析（博士、硕士）、偏微分方程（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
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
著 作
[1] Juncheng Wei, Yuanze Wu, Potentials and Partial Differential Equations-The Legacy of David R. Adams (Sharp stability of the logarithmic Sobolev inequality in the critical point setting), De Gruyter, 2023.
论 文
代表性论文：
[1] Juncheng Wei, Yuanze Wu, On the stability of the Caffarelli-Kohn-Nirenberg inequality, Mathematische Annalen, 384(2022), 1509–1546.
[2] Juncheng Wei, Yuanze Wu, Ground states of nonlinear elliptic systems with mixed couplings, Journal de Mathématiques Pures et Appliquées, 141(2020), 50–88.
[3] Juncheng Wei, Yuanze Wu, Normalized solutions for Schrodinger equations with critical Sobolev exponent and mixed nonlinearities, Journal of Functional Analysis, 283(2022), article 109574.
[4] Juncheng Wei, Yuanze Wu, Stability of the Caffarelli-Kohn-Nirenberg inequality: Existence of minimizers, Mathematische Zeitschrift, 308(2024), article 64.
[5] 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.
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] 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)
[3] Juncheng Wei, Yuanze Wu, On some Schrodinger equations in RN, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153(2023), 1503–1528.
[4] Juncheng Wei, Yuanze Wu, Infinitely many vortex solutions of the magnetic Ginzburg-Landau equation with external potentials in R2, Journal of Mathematical Physics, 62(2021), 041509, 33 pp.
[5] Yuanze Wu, Wenming Zou, On a critical Schrödinger system in R4with steep potential wells, Nonlinear Analysis, 191(2020), 111643.
[6] Juncheng Wei, Yuanze Wu, Local uniqueness of the magnetic Ginzburg-Landau equation, Journal of Elliptic and Parabolic Equations, 6(2020), 187–209. (Special Issue for Celebration of the 70th Birthday of Professor Michel Chipot)
[7] Yuanze Wu, Wenming Zou, Spikes of the two-component elliptic system in R4with thecritical Sobolev exponent, Calculus of Variations, 58(2019), article 24.
[8] 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.
[9] Yuanze Wu, Ground state of a K-component critical system with linear and nonlinear couplings: an attractive case, Advanced Nonlinear Studies, 19(2019), 595–623.
[10] Yuanze Wu, On finding the ground state solution to the linearly coupled Brezis-Nirenberg system in high dimensions: the cooperative case, Topological Methods in Nonlinear Analysis, 53(2019), 697–729.
[11] Yuanze Wu, Spikes of sign-changing solutions to the critical Schrodinger equations with trapping potentials, Applicable Analysis, 98(2019), 1027–1041.
[12] Yuanze Wu, On the semiclassical solutions of a two-component elliptic system in R4with trapping potentials and Sobolev critical exponent: the repulsive case, Zeitschrift fur angewandte Mathematik und Physik, 69(2018), 111.
[13] Yuanze Wu, Least energy sign-changing solutions of the singularly perturbed Brezis–Nirenberg problem, Nonlinear Analysis, 171(2018), 85–101.
[14] Yuanze Wu, Sign-changing semi-classical solutions of the Brezis–Nirenberg problems with jump nonlinearities in high dimensions, Journal of Mathematical Analysis and Applications, 461(2018), 7–23.
[15] Yisheng Huang, Yuanze Wu, On a Kirchhoff Equation in Bounded Domains, Advanced Nonlinear Studies, 18(2018), 613–648.
[16] Yisheng Huang, Zeng Liu, Yuanze Wu, On Kirchhoff type equations with critical Sobolev exponent, Journal of Mathematical Analysis and Applications, 462(2018), 483–504.
[17] Yuanze Wu, On a K-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case, Calculus of Variations, 56(2017), article 151.
[18] Yuanze Wu, Tsung-Fang Wu, Wenming Zou, On a two-component Bose–Einstein condensate with steep potential wells, Annali di Matematica Pura ed Applicata, 196(2017), 1695–1737.
[19] Juntao Sun, Tsung-fang Wu, Yuanze Wu, Existence of nontrivial solution for Schrodinger–Poisson systems with indefinite steep potential well, Zeitschrift fur angewandte Mathematik und Physik, 68(2017), 73.
[20] Yisheng Huang, Zeng Liu, Yuanze Wu, On a biharmonic equation with steep potential and indefinite potential, Advanced Nonlinear Studies, 16(2016),699–717.
[21] Yisheng Huang, Zeng Liu, Yuanze Wu, On finding solutions of a Kirchhoff type problem, Proceedings of the American Mathematical Society, 144(2016), 3019–3033.
[22] Yuanze Wu, Yisheng Huang, Zeng Liu, Kirchhoff type problem with potential well and indefinite potential, Electronic Journal of Differential Equations, 178(2016), 2016.
[23] Yuanze Wu, Yisheng Huang, Zeng Liu, On a Kirchhoff type problem in RN, Journal of Mathematical Analysis and Applications, 425 (2015), 548–564.
[24] 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, Communications in Contemporary Mathematics, 17 (2015), 1450045 (35 pages).
[25] Yuanze Wu, Yisheng Huang, Zeng Liu, Sign-changing solutions for Schrodinger equations with vanishing and sign-changing potentials, Acta Mathematica Scientia, 34B (2014), 691–702.
[26] Yisheng Huang, Zeng Liu, Yuanze Wu, On a nonlinear Schrödinger equation with indefinite potential, Nonlinear Analysis: Real World Applications, 17 (2014), 161–170.
[27] Yuanze Wu, Yisheng Huang, Sign-changing solutions for Schrodinger equations with indefinite supperlinear nonlinearities, Journal of Mathematical Analysis and Applications, 401 (2013), 850–860.
[28] Yuanze Wu, Yisheng Huang, Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent, Boundary Value Problems, (2013) 149 (10 pages).
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, arXiv, 2024.
[2]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, arXiv, 2025.
