司建国

  • 司建国

1958年12月生;教授、博士生导师。

  • 学术经历

  • 2003—,山东大学数学学院,教授
  • 1996—2003,滨州学院,教授
  • 1991—1995,滨州学院,副教授
  • 行政职务与学术兼职

  • 1996-2003,滨州学院数学系主任
  • 1991-1995,滨州学院数学系副主任
  • 1996—,美国《数学评论》特邀评论员,美国数学会会员
  • 2005—,山东数学学会微分方程专业委员会副理事长
  • 2011—,《Pure Mathematics》编委
  • 访问经历

  • 2002.9—2002.12,韩国仁荷大学、江南大学和中南大学,访问教授
  • 1999.3—1999.7,中国科学院数学研究所,访问教授
  • 1991.3—1992.3,中国科学院成都分院数学研究所,访问学者
  • 学习经历

  • 2001.9—2003.12,四川大学数学学院博士研究生,获理学博士学位
  • 1985.9—1987.1,华东师范大学应用数学研究生班学习
  • 1976.9—1978. 9,滨州学院数学系学习
  • 项目

  • 2012—2015,带拟周期强迫的非线性Hamilton偏微分方程拟周期解的存在性研究,国家自然科学基金委面上项目,负责人
  • 2009—2011,迭代泛函微分方程中的小除数问题和解析解的存在性与稳定性,国家自然科学基金委面上项目,负责人
  • 2006—2009,迭代泛函微分方程中的解析理论及数值解的研究山东省自然科学基金委面上项目,负责人
  • 2010—2013,带拟周期强迫的非线性Hamilton偏微分方程拟周期解的存在性,山东省自然科学基金委面上项目,负责人
  • 论著

  1. M.Zhang, Jianguo Si, C^{\infty}-solutions for a class of generalized Feigenbaum’s functional equations, Science in China, Series A-Mathematics, 2011.9, In press.
  2. Hanssmann H,Jianguo Si, Quasi-periodic solutions and stability of the equilibrium for quasi-periodically forced planar reversible and Hamiltonian systems under the Bruno condition,Nonlinearity ,23(2010),555-577.
  3. Jianguo Si,X.L.Li,Small divisors problem in dynamical systems and analytic solutions of the Shabat equation,J. Math. Anal. Appl., 367(2010), 287-295.
  4. Jianguo Si,H.Y.Zhao, Small Divisor Problem in Dynamical Systems and Analytic Solutions of a q-Difference Equation with a Singularity at the Origin, Results In Math., 58(2010),337-353.
  5. L.H.Zhang, Jianguo Si, New soliton and periodic solutions of (1+2)-dimensional nonlinear Schrodinger equation with dual-power law nonlinearity, Communication in nonlinear science and numerical simulation,15(2010),2747-2754.
  6. M. Zhang, Jianguo Si, Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing, Physica D ,238(2009),2185-2215.
  7. Jianguo Si,M.Zhang, Construction of convex solutions for the second type of Feigenbaum’s functional equations, Science in China, Series A-Mathematics, 52(2009),1617-1638 (中文版:《中国科学》, A辑, 39(2009), 49-70.)
  8. J.Liu, Jianguo Si,Analytic solutions of an iterative differential equation under Brjuno condition,Acta Math. Sinica-English Series,25(2009),1469-1482.
  9. H.Y.Zhao, Jianguo Si, Analytic solutions of a second-order iterative functional differential equation near resonance, Annales Polonici Math.,96(2009),209-226.
  10. Liu lingxia, JIanguo Si,Analytic solutions of a polynomial-like iterative functional equation near resonance, J. Math. Res. Exp., 29(2009), 737-744.
  11. Jianguo Si, Invariant tori and unboundedness for second order differential equations with asymmetric nonlinearities depending on the derivatives, Nonlinear Anal.,67(2007),3098-3115.
  12. Jianguo Si,H.Y.Zhao, Local invertible analytic solutions for an iterative differential equation related to a discrete derivatives sequence, J.Math. Anal. Appl., 335(2007), 428-442.
  13. Jianguo Si,M.H.Ma, Local invertible analytic solution of a functional differential equation with deviating arguments depending on the state derivative, J.Math.Anal.Appl., 327(2007),723-734.
  14. Jianguo Si, Invariant tori for a reversible oscillator with a nonlinear damping and periodic forcing term, Nonlinear Analysis 64 (2006) 1475 – 1495.
  15. JianGuo Si, Weinian Zhang, Analytic solutions of a second-order nonautonomous iterative functional differential equation, J. Math. Anal. Appl. 306(2005), 398-412.
  16. JianGuo Si, Weinian Zhang, Analytic solutions of a class of iterative functional differential equation, Journal of Computational and Applied Mathematics, 162(2004), 467-481.
  17. Jian-Guo Si, Weinian Zhang, Gwang-Hui Kim, Analytic solutions of a iterative functional equation , Appl. Math. Comput. 150(2004), 647-659.
  18. Bin Xu, Weinian Zhang, Jian-Guo Si, Analytic solutions of a functional equation , J. Diff. Equ. Appl., 10(2004),201-211.
  19. Jian-Guo Si, Weinian Zhang, Analytic solutions of a q-difference equation and an application to iterative functional equation , J. Diff. Equ. Appl. 10(11)(2004), 955-962.
  20. JianGuo Si, Weinian Zhang, Analytic solutions of a nonlinear iterative functional equation near neutral fixed points and poles, J. Math. Anal. Appl. 284(2003), 373-388.
  21. Jian-Guo Si, Xin-Ping Wang, Analytic solutions of a second-order iterative functional differential equation, Computers Math. Applic., 43(2002),81-90.
  22. Jian-Guo Si, Xin-Ping Wang, Wei-Nian Zhang, Analytic invariant curves for a planar map, Applied Math. Letters, 15(2002), 567-573.
  23. S.S. Cheng, J.-G. Si, X.-P. wang, An existence theorem for iterative functional differential equations, Acta Math. Hungar, 94(2002), 1-17.
  24. Jian-Guo Si, Sui Sun Cheng, Analytic solutions of a functional differential equation with proportional delays, Bull. Korean Math. Soc., 39(2002), 225-236.
  25. Jian-Guo Si, Weinian Zhang, Analytic solutions of a functional equation for invariant curves, J. Math. Anal. Appl. 259(2001), 83-93.
  26. Xin-ping Wang, Si jianguo, Analytic solutions of an iterative functional differential equation, J. Math. Anal. Appl. 262(2001), 490-498.
  27. Jian-Guo Si, Xin-Ping wang, Differential solution of a polynomial-like iterative equation with variable coefficients, Publications Math. Debrecen, 58(2001), 57-72.
  28. Xin-Ping Wang, Jian-Guo Si, Differentiable solutions of an iterative functional equation, Aequations Math., {\bf 61}(2001), 79-96.
  29. Jian-Guo Si, Analytic solutions of a neutral functional differential-difference equation, Appl. Math. E-Notes, 1(2001).
  30. Jian-Guo Si, Xin-Ping Wang, Analytic solutions of a second-order iterative functional differential equation, Journal of Computational and Applied Mathematics, 116(2000),
  31. Jian-Guo Si, Xin-Ping wang, Analytic solutions of a second-order functional differential equation with a state dependent delay, Results Math., 39(2000), 345-352.
  32. Jian-Guo Si , Xin-Ping Wang, Sui Sun Cheng , Nondecreasing and convex $C^2$-solutions of an iterative functional Differential equation, Aequations Math., 60(2000), 38-56.
  33. Jian-Guo Si, Analytic solutions of a nonlinear functional differential equation with proportional delays, Demonstratio Math. 37(4)(2000)
  34. J.G.Si, W.N.Zhang and S.S.Cheng, Smooth solutions of an iterative functional equation, Functional Equation and Inequalities, Kluwer Academic Publishers, 518(2000), 221-232.
  35. J.G.Si, W.N.Zhang and S.S.Cheng, Continuous solutions of an iterative functional inequality on compact interval, Nonlinear Studies, 1(1)(2000), 105-108.
  36. Aiqin Qi and Jianguo Si, Discussion on continuous solutions of a functional equation, Ann. Diff.Eqs., 16(1)(2000), 56-61.
  37. Jian-Guo Si, X.P.Wang and S.S.Cheng, Analytic solutions of a functional differential equation with a state derivative dependent delay, Aequationes Math.,(1999)(57),75-86.
  38. Jian-Guo Si, Xin-ping Wang, Analytic solutions of a polynomial-like iterative functional equation, Demonstratio Math.32(1)(1999), 95-103.
  39. Jian-Guo Si, Xin-Ping Wang , Analytic Solutions of a Second-order Functional Differential equation with a State Derivative Dependent Delay, Colloquium Math., 79(2)(1999),273-281.
  40. S.S.Cheng and J.G.Si, Construction of maps with prescribed periodic orbits,International J. Math. Education in Sci. \& Tech., 1999, 30(5), 750-753.
  41. Xin-Ping Wang, Jian-Guo Si, Analytic solutions of a functional equation of invariant curves, Dynamical systems, Proceeding of the international conference in honor of Prof. Liao Shantao, World Scientific, 1999, 270-274.
  42. 王新平, 司建国, 一类迭代函数方程的连续解, 数学学报, 1999, 42(5), 945-950.
  43. Jian-Guo Si, Sui Sun Cheng, Smooth solutions of an nonhomogeneous iterative functional differential equation, Proceedings of the Royal Society of Edinburgh, 128A(1998), 821-831.
  44. Si jianguo, Xin-ping Wang, Smooth solutions of an nonhomogeneous iterative functional differential equation with variable coefficients, J. Math.Anal. Appl., 226(1998), 377-392.
  45. Si Jianguo, Zhang weinian, On $C^2$ solutions of a functional equation, Acta Mathematics Sinica (New series), 43(1998),705-710.
  46. Jian-Guo Si, Sui Sun Cheng, Note on an iterative functional differential equation, Demonstratio Math,31(3)(1998),609-614.
  47. 司建国, 张伟年,一个函数方程的$C^2$类解,数学学报,1998,(41)4,1061-1064.
  48. Jian-Guo Si, Wen-rong Li, Sui Sun Cheng, Analytic solutions of an iterative functional differential equation, Computers Math. Applic., 33(1997),47-51.
  49. Jian-Guo Si, Sui Sun Cheng, Analytic solutions of a functional differential equation with statedependent argument, Taiwanese Journal of Mathematics, 1(1997), 471-480.
  50. Si Jianguo, On the monotonic continuous solutions of the iterated equation $f^N(x)=\sum_{n=0}^{N-1}A_nf^n(x),$ Demonstratio Math.29(3)(1996), 543-547.
  51. 司建国,一类迭代方程$C^1$类解的讨论, 数学学报, 1996,39(2), 247-256.
  52. 司建国, 关于高阶常系数线性中立型泛函微分方程周期解的讨论, 应用数学和力学, 17(1)(1996), 29-37.
  53. Si Jianguo, Discussion on the periodic solutions for higher-order linear equation of neutral type with constant coefficients, Applied Mathematics and Mechanics,17(1)(1996).
  54. Si Jianguo, On analytic solutions of the equation of invarint curres,C.R.Math.Rep. Acad.Sci.Canada,17(1)(1995),49-52.(加拿大)
  55. 司建国,关于迭代方程$G(f(x),f^{n_1}(x),\cdots,f^{n_k}(x))=F(x)$的连续解, 数学研究与评论,1995,15(1),149-150.
  56. 司建国, 关于迭代方程$\sum_{i=1}^n\lambda_if^i(x)=F(x)$局部的解析解的存在性, 数学学报, 1994,37(5),590-600.
  57. Si Jianguo, Discussion on the $C^n$-solutions of the iterated equation $\lambda_1f(x)+\lambda_2f^2(x)=F(x),$Acta Mathematica Scientia,1994,14(Supp.), 53-63.
  58. 司建国, 关于迭代方程$\sum_{i=1}^n\lambda_if^i(x)=F(x)$的$C^2$类解, 数学学报,1993, 36(3), 348-357.
  59. 司建国, 两类线性泛函微分方程解析解的存在性, 应用数学学报, 1991, 14(2), 262-276.
  60. 司建国, 李文荣, 关于一些函数积分方程的解析解, 纯粹数学与应用数学, 2(1991).
  61. 司建国, 一类迭代系统解的存在性和唯一性, 纯粹数学与应用数学, 2(1990).
  62. 李文荣, 司建国, 关于函数方程的连续解和解析解, 数学研究与评论, 2(1989).
  63. 司建国, 李文荣, Banach 空间中一类函数方程租的连续解的存在性和唯一性, 工程数学学报, 2(1989).
  • 研究兴趣

常微分方程定性理论、哈密顿动力系统、KAM理论、迭代泛函微分方程的解析理论.

  • 教学情况

为本科生开设课程:数学分析、常微分方程、泛函分析、实变函数、复变函数、高等代数、近世代数.

为研究生开设课程: 复动力系统、动力系统基础、微分方程的定性理论、应用微分方程、偏微分方程、微分方程专题、无穷维动力系统.

  • 已毕业研究生 (以入学时间为序)

博士研究生:张敏、赵侯宇

硕士研究生: 赵侯宇、李先龙、 刘杰、 张亭亭、王莉莉、 刘同波、马明环、刘凌霞、庄翠霞、焦爱军、胡明才、张劲、张萍萍、胡平、高丽、刘静

  • 在读研究生(以入学时间为序)

博士研究生: 脱秋菊、张立华、芮杰、邱汶华、郗强、刘杰、张亭亭

硕士研究生: 李斌、李峰巍、李燕、程红玉、娄兆伟