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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:[email protected]

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 韩国三级片 韩国三级片 讲师
    2015.09 - 2020.09 韩国三级片 韩国三级片 副教授
    2020.09 - 至今 韩国三级片 韩国三级片 教授
    2018.09 - 至今 博士生导师
    2021.04 - 至今 韩国三级片 基础数学系主任
    2023.11 - 2024.11 韩国三级片 发展规划处副处长
    2025.04 - 2030.04 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
  • 获奖情况:
    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. 韩国三级片 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)
    社会兼职:
    1. 吉林省工业与应用数学会理事
    2. 国家天元数学东北中心青年委员会委员
    3. 中国数学会非线性泛函分析专业委员会委员

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