Research

I am working in the field of research related to Analysis of Partial Differential Equations. Since my master’s studies, I have focused on Nonlinear Functional Analysis and PDEs, especially elliptic problems with nonlocal (fractional) operators. During my PhD, I studied Harmonic Analysis on two-step nilpotent Lie groups, most notably the Heisenberg group. My current interests include stability (quantitative) properties of functional inequalities on the Heisenberg group and Hyperbolic space, as well as noncommutative PDEs arising in Quantum Spaces.

Projects

• 2026.06—2029.05，一类带有 Hartree 项 Kirchhoff 方程解的存在性及相关问题研究，云南省应用基础研究计划面上项目（202601AT070048），¥100,000，Co-PI
• 2026.01—2029.12，一类椭圆方程自由边界问题解的唯一性和单调性及相关问题研究，国家自然科学基金地区项目（12561020），¥280,000，Co-PI
• 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），¥100,000，PI
• 2024.01—2028.12，兴滇英才支持计划——青年专项，¥400,000，PI
• 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），¥300,000，PI
• 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），¥50,000，PI
• 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），¥20,000，PI
• 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），¥280,000，Co-PI
• 2022.06—2027.05，云南师范大学——联大学者，¥300,000，PI
• 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），¥480,000，Co-PI

Books

• 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.
• 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.

已完成论文

1. Chen, Shaoxiong; Hajaiej, Hichem; Yang, Min and Yang, Zhipeng. “ Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators .” J. Pseudo-Differ. Oper. Appl. 49 (2026), no. 3, Article: 49.
2. Xing, Huichao; Yang, Zhipeng. “ Low-regularity well-posedness for a mixed-sign quadratic Dirac equation on N-star metric graphs .” Z. Angew. Math. Phys. 77 (2026), no. 162, 1-19.
3. Yang, Zhipeng. “ Spectral Properties of the Sub-Laplacian on 2-Step Stratified Lie Groups Without the Moore-Wolf Condition .” J. Partial Differ. Equations 39 (2026), no. 1, 70-90.
4. Gu, Guangze; Li, Ziwei; Wei, Guoyan; Yang, Zhipeng. “ Ground states for a class of generalized fractional Kirchhoff-type problem .” Differ. Integral Equ. 39 (2026), no. 3-4, 183–204.
5. Chen, Yongpeng; Yang, Zhipeng. “ Multiplicity and concentration behavior of solutions for the generalized quasilinear Schrödinger equation with critical growth .” Demonstr. Math. 58 (2025), no. 1, Paper No. 20250164.
6. Chen, Yongpeng; Yang, Zhipeng. “ Multiple positive solutions for the generalized quasilinear Schrödinger equation in RN .” Acta Math. Sci. Ser. B (Engl. Ed.) 45 (2025), no. 5, 2010–2028.
7. Luo, Jiao; Yang, Zhipeng; Zeng, Anbiao; Zhu, Ling. “ Fractional Schrödinger–Poisson system involving concave and convex nonlinearities .” Z. Anal. Anwend. 44 (2025), no. 1–2, 235–250.
8. Chen, Yongpeng; Yang, Zhipeng; Zhang, Jianjun. “ On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities .” NoDEA Nonlinear Differential Equations Appl. 32 (2025), no. 5, Paper No. 83, 26 pp.
9. Chen, Yongpeng; Yang, Zhipeng. “ Concentration of ground state solutions for critical generalized quasilinear equation with steep potential well .” Math. Methods Appl. Sci. 48 (2025), no. 1, 397–416.
10. Li, Quanqing; Yang, Zhipeng. “ Existence of normalized solutions for a Sobolev supercritical Schrödinger equation .” Electron. Res. Arch. 32 (2024), no. 12, 6761–6771.
11. 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.
12. 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.
13. Chen, Yongpeng; Yang, Zhipeng. “ Existence of multi-bump solutions for a nonlinear Kirchhoff equation .” J. Nonlinear Var. Anal. 8 (2024), 233–248.
14. 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.
15. 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.
16. 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.
17. Yang, Zhipeng. “ Critical Fujita exponent and blow-up results for the Rockland heat equation .” Acta Math. Sci. Ser. A (Chinese Ed.) 43 (2023), no. 3, 795–807.
18. 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.
19. 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.
20. Gu, Guangze; Yang, Zhipeng. “ On the singularly perturbation fractional Kirchhoff equations: critical case .” Adv. Nonlinear Anal. 11 (2022), no. 1, 1097–1116.
21. 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.
22. 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.
23. Gu, Guangze; Yang, Xianyong; Yang, Zhipeng. “ Infinitely many sign-changing solutions for nonlinear fractional Kirchhoff equations .” Appl. Anal. 101 (2022), no. 16, 5850–5871.
24. Yang, Zhipeng. “ 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.
25. 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.
26. 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.
27. Yang, Zhipeng. “ Fujita exponent and nonexistence result for the Rockland heat equation .” Appl. Math. Lett. 121 (2021), Paper No. 107386, 6 pp.
28. 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.
29. Chen, Yongpeng; Yang, Zhipeng. “ Multiplicity of solutions for a class of critical Schrödinger–Poisson system with two parameters .” Acta Math. Sci. Ser. A (Chinese Ed.) 41 (2021), no. 6, 1750–1767.
30. 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.
31. Jin, Tiankun; Yang, Zhipeng. “ The fractional Schrödinger–Poisson systems with infinitely many solutions .” J. Korean Math. Soc. 57 (2020), no. 2, 489–506.
32. Yang, Zhipeng; Yu, Yuanyang. “ Geometrically distinct solutions of nonlinear elliptic systems with periodic potentials .” Arch. Math. (Basel) 115 (2020), no. 6, 703–716.
33. 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.
34. 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.
35. Yang, Xianyong; Yang, Zhipeng. “ Existence of multiple non-trivial solutions for a nonlocal problem .” AIMS Math. 4 (2019), no. 2, 299–307.
36. Yang, Zhipeng; Zhao, Fukun. “ Three solutions for a fractional Schrödinger equation with vanishing potentials .” Appl. Math. Lett. 76 (2018), 90–95.

Activities

Honors and Awards

• Xingdian Talent, Yunnan Province, 2023.
• Excellent Thesis Award, Yunnan Province, 2020.
• Excellent Thesis Award, Yunnan Normal University, 2018.
• Yunnan Provincial Government Scholarship, Yunnan Normal University, 2017.
• The Wu Daguan Scholarship for graduate students, Yunnan Normal University, 2017.
• National Scholarship for graduate students, Yunnan Normal University, 2016.
• Outstanding Graduates Awards, Harbin Normal University, 2015.
• National Encouragement Scholarship, Harbin Normal University, 2012, 2013, 2014.

Professional Service

Talks

Conference Attended

• 2025.Aug 20-25: China-Korea Workshop on Partial Differential Equations, University of Science and Technology of China, China.
• 2025.Jul 21-25: 15th International ISAAC Congres, Nazarbayev University, Kazakhstan.
• 2025.May 23-26: International Conference on Nonlinear Analysis and 23rd National Conference on Nonlinear Functional Analysis, Jiangsu University of Technology, China.
• 2025.May 9-11: The 12th Young Scholars Forum on Partial Differential Equations, Shanxi University, China.
• 2025.Apr 25-27: Workshop on Nonlinear Partial Differential Equations, Nanjing Normal University, China, April 25-27, 2025
• 2025.Dec 8-14: Tianyuan Mathematics Research Center, China.
• 2024.Jul 19-22: 2024 Annual Conference of the Yunnan Mathematical Society, Baoshan University, China.
• 2024.Jun 9-14: Tianyuan Mathematics Research Center, China.
• 2024.May 10-13: The 11th Young Scholars Forum on Partial Differential Equations, Anhui Normal University, China.
• 2023.Dec 22-25: The 2023 Annual Conference of the Chinese Mathematical Society, Dalian University of Technology, China.
• 2023.Jul 21-24: 2023 Annual Conference of the Yunnan Mathematical Society, Chuxiong Normal University, China.
• 2023.Jul 10-12: 2023 Workshop on Harmonic Analysis, Harbin Institute of Technology, China.
• 2023.Jun 22-24: 2023 Xi’an Frontier Forum on Nonlinear Functional Analysis, Shaanxi Normal University, China.
• 2023.May 19-22: International Conference on Nonlinear Analysis and 22rd National Conference on Nonlinear Functional Analysis, Guizhou Minzu University, China.
• 2023.May 12-15: The 10th Young Scholars Forum on Partial Differential Equations, Northwestern Polytechnical University, China.
• 2022.Jul 16-18: 2022 Annual Conference of the Yunnan Mathematical Society, Zhaotong University, China.
• 2021.Jul 23-26: International Conference on Nonlinear Analysis and 21th National Conference on Nonlinear Functional Analysis,Yunnan Normal University, China.
• 2021.Feb 15-19: Conference on Microlocal and Global Analysis in Geometry and Mathematical Physics, University of Potsdam, Germany.
• 2019.Aug 7-8: Workshop on Dynamics of PDEs from Fluids and Nonlinear Waves, Nanjing University, China.
• 2019.Jun 15-17: International Workshop on Nonlinear Analysis and Reaction Diffusion equation, Harbin Normal University, China.
• 2019.May 10-12: Workshop on Nonlinear Analysis and its Applications of Young Scholars, Central China Normal University, China.
• 2019.Apr 22-26: Workshop on Emerging Areas in Reaction-diffusion Systems: Mathematical Theory and Applications to Physics, Biology and the Social Sciences, East China Normal University, China.
• 2018.Nov 30-Dec 3: 2018 Workshop on Nonlinear Analysis of Young Scholars, Yunnan Normal University, China.
• 2018.May 14-18: International Conference on Variational Methods (ICVAM-4), Chern Institute of Mathematics, Nankai University, China.
• 2018.May 11-14: International Conference on Nonlinear Analysis and 20th National Conference on Nonlinear Functional Analysis, Shanxi University, China.
• 2017.Jun 14-17: 11th East China Partial Differential Equations Conference, East China Normal University, China.
• 2017.May 25-27: International Conference on Nonlinear Functional Analysis, Yunnan Normal University, China.
• 2016.May 20-22: International Conference on Nonlinear Analysis and 19th National Conference on Nonlinear Functional Analysis, Central China Normal University, China.
• 2014.Jul 14-16: International Conference on Nonlinear Analysis and 18th National Conference on Nonlinear Functional Analysis, Harbin Normal University, China.

Teaching

• 2026级：
  • 杜兴宇
  • 胡豪
  • 金兰洁
  • 袁张敏
• 2025级：
  • 马引倩
  • 施伯佳
  • 杨江燕
  • 杨昕昕
• 2024级：
  • 任宗雄
    • 主持云南师范大学2026年度研究生科研创新基金：四元数球面上改进的Sobolev不等式.
    • Ren, Zongxiong and Yang, Zhipeng：Improved Sobolev Inequalities on the Quaternionic Sphere. arXiv:2603.28469.
    • Ren, Zongxiong and Yang, Zhipeng：Fractional Sobolev-type embedding on CR sphere and Heisenberg group. arXiv:2604.18102.
  • 谭豪
    • 主持云南师范大学2026年度研究生科研创新基金：等距群作用下闭黎曼流形上改进的分数阶Sobolev嵌入.
    • Tan, Hao; Yan, Zetian and Yang, Zhipeng：Sharp Fractional Sobolev Embeddings on Closed Manifolds. arXiv:2512.18770.
    • Tan, Hao and Yang, Zhipeng：Improved Fractional Sobolev Embeddings on Closed Riemannian Manifolds under Isometric Group Actions. arXiv:2603.28451.
• 2023级：
  • 罗娇：昆明市昆华实验中学
    • 获得2025年硕士研究生国家奖学金
    • 主持云南师范大学2025年度研究生科研创新基金：分数阶Schrödinger-Poisson系统解的存在性研究
    • Luo, Jiao and Yang, Zhipeng：Existence and concentration phenomenon of multiple solutions for the fractional logarithmic Schr\"{o} dinger-Poisson system via penalization method. arXiv:2508.16229.
    • Luo, Jiao; Yang, Zhipeng; Zeng, Anbiao; Zhu, Ling：Fractional Schrödinger–Poisson system involving concave and convex nonlinearities. Z. Anal. Anwend. 44 (2025), no.1–2, 235–250.
  • 朱灵：官渡区第二中学
    • 获得2025年硕士研究生一等奖学金
    • 主持云南师范大学2025年度研究生科研创新基金：量子图上的Dirac方程解的存在性和多重性
    • Yang, Zhipeng and Zhu, Ling：Bound states of nonlinear Dirac equation on noncompact quantum graphs with localized nonlinearities. arXiv:2505.02036.
    • Luo, Jiao; Yang, Zhipeng; Zeng, Anbiao; Zhu, Ling：Fractional Schrödinger–Poisson system involving concave and convex nonlinearities. Z. Anal. Anwend. 44 (2025), no.1–2, 235–250.
  • 曾安彪：昆明西南联大研究院附属学校
    • 获得2025年硕士研究生国家奖学金
    • Zeng, Anbiao and Gu, Guangze：Infinitely many negative energy solutions for fractional Schrödinger-Poisson systems. Appl. Math. Lett. 162 (2025), Paper No. 109389, 6 pp.
    • Luo, Jiao; Yang, Zhipeng; Zeng, Anbiao; Zhu, Ling：Fractional Schrödinger–Poisson system involving concave and convex nonlinearities. Z. Anal. Anwend. 44 (2025), no.1–2, 235–250.

• 2025年: 李仙、杨洪明、李安英获2025高教社杯全国大学生数学建模竞赛云南省一等奖
• 2025年: 尹杨梦思、吴丽兰、张惠婷获2025高教社杯全国大学生数学建模竞赛云南省一等奖
• 2024年: 霍李蕾、杨洪明、沈思仪获2024高教社杯全国大学生数学建模竞赛云南省一等奖
• 2024年: 蔡振阳、钱雨萌、李航程获2024高教社杯全国大学生数学建模竞赛云南省二等奖
• 2024年: 肖旋、张文聪、白梓辰获2024高教社杯全国大学生数学建模竞赛云南省二等奖
• 2024年: 罗梅标、龙睿、杨品洋获2024高教社杯全国大学生数学建模竞赛云南省三等奖
• 2023年: 蔡霓烁、苏春婷、环丽红获2023高教社杯全国大学生数学建模竞赛云南省三等奖

• 2026.3-2026.7: Advanced Mathematics (Calculus II)
• 2026.3-2026.7: Advanced Mathematics (Retake Class)
• 2025.9-2026.1: Advanced Mathematics (Calculus I)
• 2024.9-2025.1: Advanced Mathematics (Calculus I)
• 2023.9-2024.1: Partial Differential Equations
• 2023.9-2024.1: Advanced Mathematics (Calculus I)
• 2023.3-2023.7: Advanced Mathematics (Calculus II)

• 2025.9-2026.1: Functional Inequalities on the Heisenberg Group
• 2025.9-2026.1: An introduction to semilinear evolution equations
• 2025.3-2025.7: Nonlinear Analysis on Manifolds:Sobolev Spaces and Inequalities
• 2025.3-2025.7: Advanced Readings Seminar
• 2024.9-2025.1: Minimax Theory
• 2023.9-2024.1: Minimax Theory
• 2022.9-2023.1: Functional Analysis

APDE Seminar

Past talks