主要科研方向为常微分方程。先后主持自然科学基金青年基金一项、面上基金一项，并参与多项自然科学基金。近年来研究p-Laplacian和跳跃非线性这两个半线性谱问题，主要结论包括谱的结构、谱理论在非线性方程中的应用、谱对权函数和势函数的依赖性以及特征值的极值等问题。迄今已在国内外重要学术期刊（包括Trans. Amer. Math. Soc.，SIAM Journal on Mathematical Analysis，J. Differential Equations）上发表论文23篇，其中SCI收录20篇。
科研项目列表：
1. 动力系统量和特征值的强连续性及最优估计（基金编号11371213，2014.01- 2017.12，55万），主持。
2. 半线性谱问题及其在边值问题和动力系统中的应用（基金编号10901089，2010.01-2012.12，16万）主持。
3. 非自治微分系统的非一致行为及其稳定性（基金编号11171090，2012.01- 2015.12，45万），参与，主持人：储继峰。
4. 微分算子特征值的最优估计（基金编号11671378，2017.01-2020.12，48万），参与，主持人：孟钢。
5. 微分方程特征值和旋转数的最优估计（基金编号12071456，2021.01- 2024.12，51万），参与，主持人：孟钢。
学术论文列表：
[1] P. Yan, Dimensions of a class of high-dimensional homogeneous Moran sets and Moran classes, Progress in Natural Science, (9)12(2002) 655-660 (SCI)
[2] P. Yan, Nonresonance for one-dimensional p-Laplacian with regular restoring, J. Math. Anal. Appl., (1)285(2003) 141-154 (SCI)
[3] P. Yan and M. Zhang, Higher order nonresonance for differential equations with singularities, Math. Methods in Appl. Sciences, 26(2003) 1067-1074 (SCI)
[4] J. Lei, X. Li, P. Yan and M. Zhang, Twist character of the least amplitude periodic solution of the forced pendulum. SIAM Journal on Mathematical Analysis, (4)35(2003) 844-867 (SCI)
[5] P. Yan and M. Zhang, Periodic eigenvalues of one-dimensional p-Laplacian with indefinite weights, Tsinghua Sci. Technol, (5) 8 (2003) 533-536
[6] P. Yan and M. Zhang, Best estimates on weighted eigenvalues of one-dimensional p-Laplacian, Northeast Math. J. 19(2003) 39-50
[7] J. Lei and P. Yan, A note on conservation law of evolution equation, Mathematics Applicata, (3)16(2003) 75-81
[8] M. Garcia-Hudobro, R. Manasevich, P. Yan and M. Zhang, A p-Laplacian problem with a multi-point boundary condition, Nonlinear Analysis theory methods & Applications, (3)59(2004) 319-333 (SCI)
[9] G.Meng, P.Yan, X. Lin and M. Zhang, Non-degeneracy and periodic solutions of semilinear differential equations with deviation. Advanced Nonlinear Stud. 6 (2006) 563-590 (SCI)
[10] W. Li and P. Yan, Various half-eigenvalues of scalar p-Laplacian with indefinite integrable weights, Abstract and Applied Analysis, vol. 2009, doi: 10.1155/2009/109757 (SCI)
[11] P. Yan and M. Zhang, Rotation number, periodic Fucik spectrum and multiple periodic solutions, Communications in Contemporary Mathematics, (3)12(2010) 437-455 (SCI)
[12] G. Meng, P. Yan and M. Zhang, Spectrum of one-dimensional p-Laplacian with an indefinite intergrable weight, Mediterr. J. Math. 7 (2010) 225-248 (SCI)
[13] W. Li and P. Yan, Continuity and continuous differentiability of half-eigenvalues in potentials, Communications in Contemporary Mathematics, Vol. 12, No. 6 (2010) 977-996 (SCI)
[14] P. Yan, Extremal values of half-eigenvalues for p-Laplacian with weights in L^1 balls, Boundary Value Problems, Doi:10.1155/2010/690342 (SCI)
[15] P. Yan and M. Zhang, Continuity in weak topology and extremal problems of eigenvalues of the p-Laplacian, Trans. Amer. Math. Soc., 363 (2011), 2003-2028. (SCI)
[16] P.Yan and M. Zhang, A survey on extremal problems of eigenvalues, Abstract and Applied Analysis, vol. 2012, doi:10.1155/2012/670463 (SCI)
[17] G.Meng, P.Yan, and M. Zhang, Minimization of Eigenvalues of One-dimensional p-Laplacian with Integrable Potentials, Journal of Optimization Theory and Applications, Vol. 156, Issue 2 (2013), 294-319 (SCI)
[18] G.Meng, P.Yan, and M. Zhang, Maximization of eigenvalues of one-dimensional p-Laplacian with integrable potentials, Communications in Contemporary Mathematics, Vol. 15, No. 1 (2013), DOI: 10.1142/S0219199712500496 (SCI)
[19] W. Chen, J. Chu, P. Yan* and M. Zhang, On the Fucik spectrum of the scalar p-Laplacian with indefinite integrable weights, Boundary Value Problems, (2014) 2014:10 (SCI)
[20] G. Meng*,K. Shen, P. Yan and M. Zhang, Strong Continuity of the Lidstone Eigenvalues of the Beam Equation in Potential, Operators and Matrices, (3) 8 (2014) 889–899 (SCI)
[21] W. Chen, J. Chu, P. Yan* and M. Zhang, Complete structure of the Fucik spectrum of the p-Laplacian with integrable potentials on an interval, Communications in Contemporary Mathematics Vol. 18, No. 6 (2016), DOI: 10.1142/S0219199715500856 (SCI)
[22] G. Meng and P. Yan, Optimal lower bound for the first eigenvalue of the fourth order equation, J. Differential Equations 261 (2016) 3149–3168 (SCI)
[23] S. Guo; G. Meng, P. Yan; M. Zhang, Optimal maximal gaps of Dirichlet eigenvalues of Sturm–Liouville operators, J. Math. Phys., 2022, 63: 072701 (SCI)
清华大学
