September 2007–February 2008, University of California, San Diego (UCSD), Tsinghua University Young Faculty Overseas Training Program

Introduction to Complex Functions, Geometry and Algebra, Calculus 3, Topics in Ordinary Differential Equations, Univariate Calculus, Multivariate Calculus, Calculus A(1), and Calculus A(2). Currently the team leader for the Calculus A course.

Introduction to Complex Functions, Ping Yan, 2011, Tsinghua University Press, ISBN: 9787302242062.

Ordinary differential equations, semi-linear spectral problems involving p-Laplacian and jumping nonlinearities, with key findings on spectral structure, applications of spectral theory in nonlinear equations, dependence of spectra on weight and potential functions, and extremal eigenvalue problems.

Research Projects:

1. Strong Continuity and Optimal Estimation of Dynamical System Quantities and Eigenvalues (Grant No. 11371213, January 2014–December 2017, 550,000 CNY), Principal Investigator.

2. Semi-linear Spectral Problems and Their Applications in Boundary Value Problems and Dynamical Systems (Grant No. 10901089, January 2010–December 2012, 160,000 CNY), Principal Investigator.

3. Non-Uniform Behavior and Stability of Non-Autonomous Differential Systems (Grant No. 11171090, January 2012–December 2015, 450,000 CNY), Participant, Principal Investigator: Jifeng Chu.

4. Optimal Estimation of Eigenvalues for Differential Operators (Grant No. 11671378, January 2017–December 2020, 480,000 CNY), Participant, Principal Investigator: Gang Meng.

5. Optimal Estimation of Eigenvalues and Rotation Numbers for Differential Equations (Grant No. 12071456, January 2021–December 2024, 510,000 CNY), Participant, Principal Investigator: Gang Meng.

Papers:

[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)