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当前位置: 首 页 - 师资队伍 - 教职员工 - 基础数学系 - 教授 - 正文

魏元鸿

基本信息
  • 性别:男

    职称:教授

    所在系别:基础数学系

    是否博导:是

联系方式
  • 电子邮箱:weiyuanhong@jlu.edu.cn

研究方向
  • 动力系统、非线性分析

讲授课程
  • 本科生课程:学科导论、纯粹数学选讲、微分方程现代方法,常微分方程,线性规划,微积分,随机数学等
    研究生课程:微分方程几何理论,非线性泛函分析

工作经历
  • 2010/10-2012/08,中国科学院,数学所,博士后
    2012/08-2015/09,吉林大学,数学学院,讲师
    2015/09-2020/09,吉林大学,数学学院,副教授
    2020/09-至今,吉林大学,数学学院,教授
    2018/09-至今,博士生导师
    2021/04-至今,吉林大学数学学院基础数学系主任
    2023/11/09-2024/11/08,吉林大学,发展规划处副处长
    2025/04/24-2030/04/23,吉林国家应用数学中心副主任

科研项目
  • 1. 国家外国专家局个人类项目(S类),2025/01-2026/12.
    2. 国家自然科学基金面上项目,2026/01-2029/12.
    3. 科技部高端外国专家引进计划,2023/01-2024/12.
    4. 国家自然科学基金面上项目,2023/01-2026/12.
    5. 国家自然科学基金面上项目,2019/01-2022/12.
    6. 国家自然科学基金面上项目,2020/01-2023/12.
    7. 国家自然科学基金面上项目,2017/01-2020/12.
    8. 国家自然科学基金青年基金,2014/01-2016/12.
    9. 吉林省教育厅科学研究项目(重点项目),2026/01-2027/12.
    10. 吉林省教育厅科学研究项目,2022/01-2023/12.
    11. 吉林省科技厅自然科学基金(学科布局项目),2020/01-2022/12.
    12. 吉林省科技厅优秀青年人才基金项目,2017/01-2018.12.

代表性成果
  • 1. On existence and concentration of solutions for fractional logarithmic Schrödinger equation with steep porential well,ESAIM: Control, Optimisation and Calculus of Variations,32(2026)17. (Joint work with Baihong Li, Dimitri Mugnai and Yuanling Sun)
    2. Existence of infinitely many periodic solutions to the nonlinear Dirac-Klein-Gordon system,DISCRETE CONT DYN-A,(2026) (Joint work with Hongying Wang and Yanheng Ding)
    3. Multiple normalized solutions for the nonlinear Choquard equation in the Aharonov–Bohm magnetic field,Z. Angew. Math. Phys. 77 (2026), no. 3, Paper No. 92. (Joint work with Baihong Li)
    4. Non-trivial periodic pattern of the nonlinear singular coupled Gierer-Meinhardt system, Commun. Nonlinear Sci. Numer. Simul. 158 (2026), Paper No. 109797. (Joint work with Hongying Wang and Kewei Zhang)
    5. On the Benci–Cerami problem for fractional Kirchhoff equation in low dimension,J. Fixed Point Theory Appl. 28 (2026), no. 1, Paper No. 6. (Joint work with Baihong Li)
    6. Well–posedness and wave breaking of solutions for the Degasperis–Procesi equation including Coriolis effects,J. Differential Equations 459 (2026), 114077. (Joint work with Joachim Escher and Baihong Li)
    7. Fractional Schrodinger equation involving a nonlinearity dependent on a lower-order fractional term. Discrete and Continuous Dynamical Systems-Series S. 2025(18):3302-3321. (Joint work with Xu Dong)
    8. On bound states of Schrödinger equation with vanishing magnetic potential. Calc. Var. Partial Differential Equations 64 (2025), no. 5, Paper No. 144, 21 pp. (Joint work with Baihong Li)
    9. Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion. NoDEA Nonlinear Differential Equations Appl. 32 (2025), no. 5, Paper No. 92. (Joint work with Joachim Escher and Baihong Li)
    10. The energy level transition for nonlinear Kirchhoff equation under a perturbation of potential. Ann. Physics 475(2025), Paper No. 169949, 19pp. (Joint work with Baihong Li)
    11. Liouville theorems for elliptic equations involving regional fractional Laplacian with order in (0, 1/2). Differential and Integral Equations, 38(2025), no. 1-2, 1-22. (Joint work with Huyuan Chen)
    12. On some regularity properties of mixed local and nonlocal elliptic equations. J. Differential Equations, 416(2025), 576–613. (Joint work with Xifeng Su, Enrico Valdinoci and Jiwen Zhang)
    13. Sparse gradient bounds for divergence form elliptic equations. J. Differential Equations, 413(2024), 606–631. (Joint work with Olli Saari and Hua-yang Wang)
    14. Multiple solutions for mixed local and nonlocal elliptic equations. Math. Z. 308 (2024), no. 40, 1-37. (Joint work with Xifeng Su, Enrico Valdinoci and Jiwen Zhang)
    15. Regularity results for solutions of mixed local and nonlocal elliptic equations. Math. Z. 302 (2022), no. 3, 1855–1878. (Joint work with Xifeng Su, Enrico Valdinoci and Jiwen Zhang)
    16. Superlinear elliptic equation with mixed boundary value in annular domain. Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 10, 1549–1559. (Joint work with Jian Tian)
    17. Liouville property of fractional Lane-Emden equation in general unbounded domain. Adv. Nonlinear Anal. 10 (2021), no. 1, 494–500. (Joint work with Ying Wang)
    18. Radial solution of asymptotically linear elliptic equation with mixed boundary value in annular domain. J. Appl. Anal. Comput. 10 (2020), no. 6, 2787–2805. (Joint work with Jian Tian)
    19. Asymptotically linear and superlinear elliptic equations with gradient terms. Electron. J. Differential Equations 2020, Paper No. 99, 14 pp. (Joint work with Jian Tian)
    20. Nondegeneracy of solutions for a critical Hartree equation. Nonlinear Anal. 199 (2020), 111969, 12 pp. (Joint work with Jacques Giacomoni and Minbo Yang)
    21. Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains. Nonlinear Anal. 187 (2019), 93–109. (Joint work with Xu Dong)
    22. On a class of non-local elliptic equations with asymptotically linear term. Discrete Contin. Dyn. Syst. 38 (2018), no. 12, 6287–6304. (Joint work with Xifeng Su)
    23. On concentration of semi-classical solitary waves for a generalized Kadomtsev-Petviashvili equation. Discrete Contin. Dyn. Syst. Ser. S 10 (2017), no. 5, 1095–1106. (Joint work with Yong Li and Xue Yang)
    24. Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian. Calc. Var. Partial Differential Equations 52 (2015), no. 1-2, 95–124. (Joint work with Xifeng Su)
    25. Existence and uniqueness of periodic solutions for second order differential equations. J. Funct. Spaces 2014, Art. ID 246258, 5 pp.
    26. Existence of solutions for singularly perturbed Hamiltonian elliptic systems with nonlocal nonlinearities. Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 385–402. (Joint work with Minbo Yang)
    27. Existence of solutions for a system of diffusion equations with spectrum point zero. Z. Angew. Math. Phys. 65 (2014), no. 2, 325–337. (Joint work with Minbo Yang)
    28. Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities. Z. Angew. Math. Phys. 65 (2014), no. 1, 41–68. (Joint work with Minbo Yang and Yanheng Ding)
    29. Existence and multiplicity of solutions for nonlinear Schrödinger equations with magnetic field and Hartree type nonlinearities. J. Math. Anal. Appl. 403 (2013), no. 2, 680–694. (Joint work with Minbo Yang)
    30. Multiplicity results for some fourth-order elliptic equations. J. Math. Anal. Appl. 385(2012)797-807.

奖励与荣誉
  • 1. 吉林省自然科学学术成果奖,二等奖,2018(第一完成人)
    2. 国家天元数学东北中心优秀青年学者,2019
    3. 吉林大学唐敖庆青年人才奖励基金,2020
    4. 高等学校优秀科研成果认定,非线性混合局部-非局部椭圆方程解的正则性研究,重大成果,2023(第一完成人)

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