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

• 2026.01—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

• 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.
• 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.
• 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.
• 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.
• 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.
• Li, Quanqing; Yang, Zhipeng. “ Existence of normalized solutions for a Sobolev supercritical Schrödinger equation .” Electron. Res. Arch. 32 (2024), no. 12, 6761–6771.
• 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.
• 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.
• Chen, Yongpeng; Yang, Zhipeng. “ Existence of multi-bump solutions for a nonlinear Kirchhoff equation .” J. Nonlinear Var. Anal. 8 (2024), 233–248.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Gu, Guangze; Yang, Zhipeng. “ On the singularly perturbation fractional Kirchhoff equations: critical case .” Adv. Nonlinear Anal. 11 (2022), no. 1, 1097–1116.
• 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.
• 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.
• Gu, Guangze; Yang, Xianyong; Yang, Zhipeng. “ Infinitely many sign-changing solutions for nonlinear fractional Kirchhoff equations .” Appl. Anal. 101 (2022), no. 16, 5850–5871.
• 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.
• 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.
• 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.
• Yang, Zhipeng. “ Fujita exponent and nonexistence result for the Rockland heat equation .” Appl. Math. Lett. 121 (2021), Paper No. 107386, 6 pp.
• 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.
• 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.
• 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.
• Jin, Tiankun; Yang, Zhipeng. “ The fractional Schrödinger–Poisson systems with infinitely many solutions .” J. Korean Math. Soc. 57 (2020), no. 2, 489–506.
• Yang, Zhipeng; Yu, Yuanyang. “ Geometrically distinct solutions of nonlinear elliptic systems with periodic potentials .” Arch. Math. (Basel) 115 (2020), no. 6, 703–716.
• 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.
• 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.
• Yang, Xianyong; Yang, Zhipeng. “ Existence of multiple non-trivial solutions for a nonlocal problem .” AIMS Math. 4 (2019), no. 2, 299–307.
• Yang, Zhipeng; Zhao, Fukun. “ Three solutions for a fractional Schrödinger equation with vanishing potentials .” Appl. Math. Lett. 76 (2018), 90–95.

Teaching

• 2025级: 施伯佳、杨江燕
• 2024级: 任宗雄、谭豪
• 2023级: 罗娇、朱灵、曾安彪

• 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)

• 2025.3-2025.7: Advanced Readings Seminar（M0701B601）
• 2024.9-2025.1: Minimax Theory（M0701X311）
• 2023.9-2024.1: Minimax Theory（M0701X311）
• 2022.9-2023.1: Functional Analysis

APDE Seminar

Past talks