姓   名：杨志鹏

职   称：副教授

人才称号：云南省兴滇英才——青年学者

工作单位：云南师范大学数学学院

电子邮箱：yangzhipeng326@163.com

研究方向及招生情况

l 研究领域：非线性泛函分析、非交换调和分析

l 招生专业：非线性分析（硕士）；偏微分方程（硕士）

工作经历

n 2024.11——至今，云南师范大学，副教授

n 2022.06——2024.11，云南师范大学，讲师

n 2019.10——2022.04，Georg-August Universität Göttingen, Mathematisches Institut, 助理研究员

教育经历

u 2019.09——2022.03，Georg-August Universität Göttingen，基础数学，博士 

u 2015.09——2018.06，云南师范大学，基础数学，硕士

u 2011.09——2015.06，哈尔滨师范大学，数学与应用数学，本科

获奖情况

u 2020 云南省优秀毕业论文

u 2018 云南师范大学优秀毕业论文

u 2017 云南省政府奖学金

u 2017 伍达观奖学金

u 2016 国家奖学金

u 2015 哈尔滨师范大学优秀毕业生/优秀毕业论文

学术兼职

² 欧洲数学会会员、中国数学会会员

² 美国数学评论、德国数学文摘评论员

² 期刊审稿人：Acta Mathematica Scientia、Annali della Scuola Normale Superiore di Pisa, Classe di Scienze、Applied Mathematics Letters、Boundary Value Problems、Complex Variables and Elliptic Equations、Discrete and Continuous Dynamical Systems-A、Discrete and Continuous Dynamical Systems-S、Journal of Geometric Analysis、Journal of Mathematical Physics、Qualitative Theory of Dynamical Systems、Mathematical Methods in the Applied Sciences、Zeitschrift für angewandte Mathematik und Physik

科研项目

v 2024.03—2027.02，齐次群上的积分不等式及其应用，云南省应用基础研究计划面上项目（202401AU070123），10万，主持

v 2024.01—2028.12，兴滇英才支持计划——青年专项，40万，主持

v 2024.01—2026.12，二步分层李群上的Hardy不等式及相关问题研究，国家自然科学基金青年项目（12301145），30万，主持

v 2023.06—2026.06，一类非局部椭圆型方程组解的存在性和渐近行为研究，云南省应用基础研究计划青年项目（202301AU070144），5万，主持

v 2023.03—2025.02，带有Kirchhoff项的椭圆型方程组的极小能量解，云南省教育厅科学研究项目（2023J0199），2万，主持

v 2023.01—2026.12，两类强不定变分问题解的存在性及相关问题研究，国家自然科学基金地区项目（12261107），28万，参与

v 2022.06—2027.05，云南师范大学——联大学者，30万，主持

v 2018.01—2021.12，非局部椭圆型方程（组）解的多重性及性态研究，国家自然科学基金面上项目（11771385），48万，参与

著作

1、杨志鹏，二部幂零李群上的调和分析（英文版），中国科学技术大学出版社，2023

2、杨志鹏、王洪杰、赵健巍，高等数学简明教程，哈尔滨工业大学出版社，2024

论文

1.  Yang, Zhipeng; Zhao, FukunThree solutions for a fractional Schrödinger equation with vanishing potentials.Appl. Math. Lett. 76 (2018), 90–95.

2. Yang, Zhipeng; Yu, Yuanyang; Zhao, Fukun The concentration behavior of ground state solutions for a critical fractional Schrödinger-Poisson system. Math. Nachr. 292 (2019), no. 8, 1837–1868.

3. Yang, Zhipeng; Yu, Yuanyang; Zhao, Fukun Concentration behavior of ground state solutions for a fractional Schrödinger-Poisson system involving critical exponent. Commun. Contemp. Math. 21 (2019), no. 6, 1850027, 46 pp.

4. Yang, Xianyong; Yang, Zhipeng Existence of multiple non-trivial solutions for a nonlocal problem. AIMS Math. 4 (2019), no. 2, 299–307.

5. Chen, Shaoxiong; Li, Yue; Yang, Zhipeng Multiplicity and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), no. 1, Paper No. 33, 35 pp.

6. Jin, Tiankun; Yang, Zhipeng The fractional Schrödinger-Poisson systems with infinitely many solutions. J. Korean Math. Soc. 57 (2020), no. 2, 489–506.

7. Yang, Zhipeng; Yu, Yuanyang Geometrically distinct solutions of nonlinear elliptic systems with periodic potentials. Arch. Math. (Basel) 115 (2020), no. 6, 703–716.

8. Yang, Zhipeng; Zhao, Fukun Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth. Adv. Nonlinear Anal. 10 (2021), no. 1, 732–774.

9. Yang, Zhipeng; Zhang, Wei; Zhao, Fukun Existence and concentration results for fractional Schrödinger-Poisson system via penalization method. Electron. J. Differential Equations 2021, Paper No. 14, 31 pp.

10. Yang, Zhipeng Fujita exponent and nonexistence result for the Rockland heat equation. Appl. Math. Lett. 121 (2021), Paper No. 107386, 6 pp.

11.  Yang, Zhipeng; Yu, Yuanyang Existence and concentration of solution for Schrödinger-Poisson system with local potential. Partial Differ. Equ. Appl. 2 (2021), no. 4, Paper No. 47, 22 pp.

12.  Chen, Yongpeng; Yang, Zhipeng Multiplicity of solutions for a class of critical Schrödinger-Poisson system with two parameters. (Chinese) Acta Math. Sci. Ser. A (Chinese Ed.) 41 (2021), no. 6, 1750–1767.

13.  Gu, Guangze; Yang, Zhipeng Positive eigenfunctions of a class of fractional Schrödinger operator with a potential well. Differential Integral Equations 35 (2022), no. 1-2, 123–150.

14. Yang, Zhipeng Non-degeneracy of positive solutions for fractional Kirchhoff problems: high dimensional cases. J. Geom. Anal. 32 (2022), no. 4, Paper No. 139, 24 pp.

15. Gu, Guangze; Yang, Zhipeng On the singularly perturbation fractional Kirchhoff equations: critical case. Adv. Nonlinear Anal. 11 (2022), no. 1, 1097–1116.

16. Yang, Zhipeng; Zhao, Fukun; Zhao, Shunneng Existence and multiplicity of normalized solutions for a class of fractional Schrödinger-Poisson equations. Ann. Fenn. Math. 47 (2022), no. 2, 777–790.

17. Chen, Yongpeng; Yang, Zhipeng Existence and asymptotical behavior of multiple solutions for the critical Choquard equation. J. Geom. Anal. 32 (2022), no. 9, Paper No. 238, 34 pp.

18. Gu, Guangze; Yang, Xianyong; Yang, Zhipeng Infinitely many sign-changing solutions for nonlinear fractional Kirchhoff equations. Appl. Anal. 101 (2022), no. 16, 5850–5871.

19. Yang, Zhi Peng A note on the heat kernel for the rescaled harmonic oscillator from two step nilpotent Lie groups. Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 9, 1597–1611.

20. Yang, Zhipeng; Zhai, Hao; Zhao, Fukun On the fractional Kirchhoff equation with critical Sobolev exponent. Appl. Math. Lett. 141 (2023), Paper No. 108596, 8 pp.

21. Gu, Guangze; Mu, Changyang; Yang, Zhipeng Existence and multiplicity of solutions for a fractional Schrödinger-Poisson system with subcritical or critical growth. Qual. Theory Dyn. Syst. 22 (2023), no. 2, Paper No. 63, 39 pp.

22. Yang, Zhipeng Critical Fujita exponent and blow-up results for the Rockland heat equation. (Chinese) Acta Math. Sci. Ser. A (Chinese Ed.) 43 (2023), no. 3, 795–807.

23. Chen, Yongpeng; Yang, Zhipeng The existence of multiple solutions for a class of upper critical Choquard equation in a bounded domain. Demonstr. Math. 57 (2024), no. 1, Paper No. 20230152. 35J20 (35J61 35S05).

24. Gu, Guangze; Mu, Changyang; Yang, Zhipeng Existence of Ground State Solutions for a Class of Non-Autonomous Fractional Kirchhoff Equations. Fractal and Fractional. 8(2024), no. 2: 113.

25. Chen, Yongpeng; Yang, Zhipeng Existence of multi-bump solutions for a nonlinear Kirchhoff equation, J. Nonlinear Var. Anal. 8 (2024), 233-248.

26. Chen, Yongpeng; Yang, Zhipeng Concentration of ground state solutions for critical generalized quasilinear equation with steep potential well, Math. Methods Appl. Sci. online, 2024.

27. Mu, Changyang; Yang, Zhipeng; Zhang, Wei Existence and concentration of solutions for a fractional Schrödinger-Poisson system with discontinuous nonlinearity. Adv. Nonlinear Stud. 24 (2024), no. 4, 992–1011.

指导学生

² 2024级：任宗雄、谭豪

² 2023级：罗娇、朱灵、曾安彪