刘兆理

 

      职       称: 教授、博导 
      学       位: 博士 
      毕业院校: 山东大学 
      研究方向: 非线性分析
      办  公  室: 本部教二楼502室
      所在部门: 数学系  
      职       务: 系主任
      电       话:  
      电子邮件: zliu@cnu.edu.cn

 

 

 

 

教学活动

开课时间

课程名称

授课对象

2019年秋季

泛函分析

研究生

2019年春季

非线性分析方法

研究生

2018年秋季

高等分析

本科生

2018年秋季

现代变分方法

研究生

2018年春季

变分方法与非线性微分方程

研究生

2016年秋季

数学分析

本科生

2013年秋季

临界点理论及其应用

研究生

2013年秋季

非线性泛函分析

研究生

2013年春季

高等分析

本科生

2012年秋季

高等分析

本科生

2012年秋季

非线性泛函分析

研究生

2012年春季

微分方程中的变分方法

研究生

2011年秋季

变分方法与非线性微分方程

研究生

2011年秋季

临界点理论及其应用

研究生

2011年秋季

分析选讲

本科生

2011年春季

临界点理论及其应用

研究生

2010年秋季

泛函分析

研究生

2010年春季

非线性泛函分析

研究生

2009年秋季

泛函分析

研究生

2009年春季

泛函分析

研究生

2009年春季

变分方法与非线性微分方程

研究生

2008年秋季

变分方法与非线性微分方程

研究生

2008年春季

非线性泛函分析

研究生

2007年春季

非线性泛函分析

研究生

2006年秋季

泛函分析

研究生

2006年春季

非线性分析方法

研究生

2005年春季

非线性泛函分析

研究生

 

主要论著

70. Vector solutions with prescribed component-wise nodes for a schrodinger system (with Zhi-Qiang Wang)

Analysis in Theory and Applications, 35 (2019), 288-311.

69. Multiple positive solutions of elliptic systems in exterior domains (with Haidong Liu)

Communications in Contemporary Mathematics, 2018, DOI: 10.1142/S0219199717500638.

68. A variant of Clark's theorem and its applications for nonsmooth functionals without the Palais-Smale condition (with Shaowei Chen and Zhi-Qiang Wang)

SIAM Journal on Mathematical Analysis, 49 (2017), 446-470.

67. Existence results for a singular quasilinear elliptic equation (with Yongtao Jing and Zhi-Qiang Wang)

Journal of Fixed Point Theory and Applications, 19 (2017), 67-84.

66. Multiple solutions of a parameter-dependent quasilinear elliptic equation (with Yontao Jing and Zhi-Qiang Wang)

Calculus of Variations and Partial Differential Equations, 2016, DOI

10.1007/s00526-016-1067-7.

65. Infinitely many sign-changing solutions for the nonlinear Schrodinger-Poisson system (with Zhi-Qiang Wang and Jianjun Zhang)

Annali di Matematica Pura ed Applicata, 195 (2016), 775-794.

64. Positive solutions of a nonlinear Schrodinger system with nonconstant potentials (with Haidong Liu)

Discrete and Continuous Dynamical Systems-A, 36 (2016), 1431-1464.

63. Elliptic systems with a partially sublinear local term (with Yongtao Jing)

Journal of Mathematical Study, 48 (2015), 290-305.

62. On Clark's theorem and its applications to partially sublinear problems (with Zhi-Qiang Wang)

Annales de l'Institut Henri Poincare-Analyse Non Lineaire, 32 (2015), 1015-1037.

61. Infinitely many solutions of p-sublinear p-Laplacian equations (with Yongtao Jing)

Journal of Mathematical Analysis and Applications, 429 (2015), 1240-1257.

60. Existence and uniqueness of positive solutions of nonlinear Schrodinger systems (with Haidong Liu and Jinyong Chang)

Proceedings of the Royal Society of Edinburgh, 145A (2015), 365-390.

59. Ground states of a nonlinear Schrodinger system with nonconstant potentials (with Haidong Liu)

Science China: Mathematics, 58 (2015), 257-278.

58. Perturbed elliptic equations with

oscillatory nonlinearities (with Zuji Guo)

Discrete and Continuous Dynamical Systems-A, 32 (2012), 3567-3585.

57. Bifurcation surfaces stemming from the Fucik spectrum (with Chong Li and Shujie Li)

Journal of Functional Analysis, 263 (2012), 4059-4080.

56. Radial solutions of a supercritical elliptic equation with Hardy potential (with Zuji Guo)

Advanced Nonlinear Studies, 12 (2012), 49-66.

55. Multi-bubble solutions for equations of CKN type (with Lishan Lin)

Communications in Contemporary Mathematics, 13 (2011), 945-968.

54. Exact number of solutions of a prescribed mean curvature equation (with Weisheng Li)

Journal of Mathematical Analysis and Applications, 367 (2010), 486-498

53. Ground states and bound states of a nonlinear Schrodinger system (with Zhi-Qiang Wang)

Advanced Nonlinear Studies, 10 (2010), 175-193.

52. Ground states of nonlinear Schrodinger Systems (with Jinyong Chang)

Proceedings of the American Mathematical Society, 138 (2010), 687-693.

51. Multi-bump solutions and multi-tower solutions for equations on R^N (with Lishan Lin)

Journal of Functional Analysis, 257 (2009), 485-505.

50. Solutions of elliptic problems with nonlinearities of linear growth (with Jiabao Su and Zhi-Qiang Wang)

Calculus of Variations and Partial Differential Equations, 35 (2009), 463-480.

49. Multi-bump solutions for a semilinear Schrodinger equation (with Lishan Lin and Shaowei Chen)

Indiana University Mathematics Journal, 58 (2009), 1659-1689.

48. Sign changing solutions with clustered layers near the origin for singularly perturbed semilinear elliptic problems on a ball (with Yihong Du, Angela Pistoia, and Shusen Yan)

Methods and Applications of Analysis, 15 (2008), 137-148.

47. A twist condition and periodic solutions of Hamiltonian systems (with Jiabao Su and Zhi-Qiang Wang)

Advances in Mathematics, 218 (2008), 1895-1913.

46. Multiple bound states of nonlinear Schrodinger systems (with Zhi-Qiang Wang)

Communications in Mathematical Physics, 282 (2008), 721-731.

45. Nodal solutions of a perturbed elliptic problem (with Yi Li and Chun-Shan Zhao)

Topological Methods in Nonlinear Analysis, 32 (2008), 49-68.

44. On the Fucik spectrum (with Chong Li, Shujie Li, and Jianzhong Pan)

Journal of Differential Equations, 244 (2008), 2498-2528.

43. Existence of type (II) regions and convexity and concavity of potential functionals corresponding to jumping nonlinear problems (with Chong Li and Shujie Li)

Calculus of Variations and Partial Differential Equations, 32 (2008), 237-251.

42. Sign-changing solutions of nonlinear elliptic equations (with Zhi-Qiang Wang)

Frontiers of Mathematics in China, 3 (2008), 221-238

41. Bounded resonance problem for semilinear elliptic equations (with Jia-Bao Su)

Discrete and Continuous Dynamical Systems, 19 (2007), 431-445

40. Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents (with Shu-Jie Li)

Topological Methods in Nonlinear Analysis, 28 (2006), 235-262

39. Multiple solutions of nonlinear Schroedinger equations via flow invariance and Morse theory (with Zhi-Qiang Wang and Tobias Weth)

Proceedings of the Royal Society of Edinburgh, 136A (2006), 945-969

38. Compactness results for Schroedinger equations with asymptotically linear terms (with Jia-Bao Su and Tobias Weth)

Journal of Differential Equations, 231 (2006) 501–512.

37. Nodal type bound states of Schroedinger equations via invariant set and minimax methods (with Francois A. van Heerden and Zhi-Qiang Wang)

Journal of Differential Equations, 214 (2005), 358-390.

36. Nodal solutions of a superlinear elliptic $p$-Laplacian equation (with Thomas Bartsch and Tobias Weth)

Proceedings of the London Mathematical Society, 91 (2005), 129-152.

35. Multi-bump type nodal solutions having a prescribed number of nodal domains: I (with Zhi-Qiang Wang)

Annales de l'Institut Henri Poincare-Analyse Non Lineaire, 22 (2005), 597-608.

34. Multi-bump type nodal solutions having a prescribed number of nodal domains: II (with Zhi-Qiang Wang)

Annales de l'Institut Henri Poincare-Analyse Non Lineaire, 22 (2005), 609-631.

33. An elliptic problem with jumping nonlinearities (with Jing-Xian Sun)

Nonlinear Analysis, Theory, Method and Application, 63 (2005), 1070-1082.

32. Schroedinger equations with concave and convex nonlinearities (with Zhi-Qiang Wang)

Zeitschrift fur Angewandte Mathematik und Physik, 56 (2005), 609-629.

31. Solutions of some nonlinear elliptic problems with perturbation terms of arbitrary growth (with Jia-Bao Su)

Discrete and Continuous Dynamical Systems, 10 (2004), 617-634.

30. Location and critical groups of critical points with an application to nonlinear eigenvalue problems (with Thomas Bartsch)

Advances in Differential Equations, 9 (2004), 645-676.

29. Multiple sign changing solutions of a quasilinear elliptic eigenvalue problem involving the $p$-Laplacian (with Thomas Bartsch)

Communications in Contemporary Mathematics, 6 (2004), 245-258.

28. On a superlinear elliptic $p$-Laplacian equation (with Thomas Bartsch)

Journal of Differential Equations, 198 (2004), 149-175.

27. Sign-changing solutions of superlinear Schr/"odinger equations (with Thomas Bartsch and Tobias Weth)

Communications in Partial Differential Equations, 29 (2004), 25-42.

26. Existence of a positive solution of an elliptic equation on $/mathbb R^N$ (with Zhi-Qiang Wang)

Proceedings of the Royal Society of Edinburgh, 134A (2004), 191-200.

25. On the Ambrosetti-Rabinowitz superlinear condition (with Zhi-Qiang Wang)

Advanced Nonlinear Studies, 4 (2004), 563-574.

24. Nontrivial solutions for perturbed $p$-Laplacian on ${/cal R}^N$ (with Jia-Bao Su)

Mathematische Nachrichten, 248-249 (2003), 190-199.

23. Contractibility of the level sets of the functionals associated with some elliptic boundary value problems and applications (with Shu-Jie Li)

Nonlinear Differential Equations and Applications, 10 (2003), 133-170.

22. Localized critical points in Banach spaces and sign changing solutions of nonlinear $p$-Laplacian equations

in: Topology Methods, Variational Methods and Their Applications---ICM 2002 Satellite Conference on Nonlinear Functional Analysis, ed. H. Brezis, K.C. Chang, S.J. Li and P. Rabinowitz, World Scientific Co., New Jersey, 2003, pp 151-158.

21. Number of invariant sets of descending flow with applications in critical point theory (with Jing-Xian Sun)

in: Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations-Lectures at Morningside Center of Mathematics, ed. H. Brezis, S.J. Li, J.Q. Liu, and P.H. Rabinowitz, International Press, New York, 2003, pp 139--156.

20. Multiplicity of solutions of semilinear elliptic boundary value problems with jumping nonlinearities at zero

Nonlinear Analysis, Theory, Method and Application, 48 (2002), 1051-1063.

19. Four versus two solutions of semilinear elliptic boundary value problems (with Jing-Xian Sun)

Calculus of Variations and Partial Differential Equations, 14 (2002), 319-327.

18. Positive solutions of a class of nonlinear elliptic eigenvalue problems

Mathematische Zeitschrift, 242 (2002), 663-686.

17. Perturbations of symmetric eigenvalue problems (with Yong-Qing Li)

Applied Mathematics Letters, 15 (2002), 903-906.

16. Perturbations from symmetric elliptic boundary value problems (with Shu-Jie Li)

Journal of Differential Equations, 185 (2002), 271-280.

15. A class of two-point boundary value problems (with Xue-Mei Zhang)

Journal of Mathematical Analysis and Applications, 254 (2001), 599-617.

14. Invariant sets of descending flow in critical point theory with applications to nonlinear differential equations (with Jing-Xian Sun)

Journal of Differential Equations, 172 (2001), 257-299.

13. Properties of positive solutions of a nonlinear eigenvalue problem (with Yong-Qing Li)

Zeitschrift fur Angewandte Mathematik und Physik, 52 (2001), 433-447.

12. Exact number of solutions of a class of two-point boundary value problems involving concave and convex nonlinearities

Nonlinear Analysis, Theory, Method and Application, 46 (2001), 181-197.

11. Positive solutions of elliptic boundary value problems without (P.S.) type assumption (with Shu-Jie Li and Zhi-Qiang Wang)

Indiana University Mathematical Journal, 50 (2001), 1347-1369.

10. Solutions of an elliptic eigenvalue problem involving subcritical and critical exponents (with Yong-Qing Li)

Communications in Partial Differential Equations, 26 (2001), 2227-2248.

9. On the existence of positive solutions of a elliptic boundary value problem (with Fu-Yi Li)

Chinese Annals of Mathematics, 21B (2000), 499-510.

8. On the existence of periodic solutions for a nonlinear system of ordinary differential equations,

Acta Mathematica Sinica, English version: 16 (2000), 505-514; Chinese version: 43 (2000), 947-954.

7. Multiple and sign-changing solutions of an elliptic eigenvalue problem with constraint (with Yong-Qing Li)

Sciences in China, Chinese version: 30 (2000), 967-975. English version: 44 (2001), 48-57.

6. Positive solutions of superlinear elliptic equations

Journal of Functional Analysis, 167 (1999), 370-398.

5. Multiple positive solutions of some nonlinear operator equations and applications (with Fu-Yi Li)

Acta Mathematica Sinica, 41 (1998), 97-102 (in Chinese).

4. Multiple positive solutions of nonlinear two-point boundary value problems (with Fu-Yi Li)

Journal of Mathematical Analysis and Applications, 203 (1996), 610-625.

3. Periodic solutions for nonlinear $n$th-order ordinary differential equations

Journal of Mathematical Analysis and Applications, 204 (1996), 46-64.

2. Methods of Functional Analysis in Nonlinear Ordinary Differential Equations (with Da-Jun Guo, Jing-Xian Sun)

Shandong Science and Technology Press, 1995, Jinan, 247pp (in Chinese).

1. Calculus of variations and super- and sub-solutions in reversed order (with Jing-Xian Sun)

Acta Mathematica Sinica, 37 (1994), 512-514, (in Chinese).

 

科研项目

开始时间

截止时间

项目名称

资金来源

2017.1

2020.12

国家自然科学基金面上项目

国家自然科学基金委

2014.1

2018.12

国家自然科学基金重点项目子项目

国家自然科学基金委

2013.1

2016.12

国家自然科学基金面上项目

国家自然科学基金委

2010.1

2012.12

北京市高等学校“高层次人才”项目

北京市教委

2009.1

2013.12

国家自然科学基金重点项目子项目

国家自然科学基金委

2009.1

2012.12

国家杰出青年科学基金

国家自然科学基金委

2006.1

2006.12

人事部留学人员科技活动择优资助项目

国家人事部

2006.1

2006.12

教育部留学回国基金

国家教育部

2006.1

2008.12

北京市教委重点项目

北京市教委

2005.1

2007.12

北京市高等学校“创新拔尖人才”项目

北京市教委

2005.1

2008.12

国家自然科学基金面上项目

国家自然科学基金委

2004.1

2004.12

国家自然科学基金专项基金项目

国家自然科学基金委

 

所获奖励

获奖时间

所获奖励与荣誉称号

2012

首都劳动奖章

2011

北京市教育工会教育先锋教书育人标兵

2011

国务院特殊津贴

2010

北京市优秀博士学位论文指导教师

2009

教育部“奖励计划”特聘教授

2008

新世纪百千万人才工程北京市市级人选

2008

国家杰出青年科学基金

2008

教育部高校自然科学二等奖

2006

北京市特聘教授

2002

山东省自然科学二等奖

1998

山东省科学技术进步一等奖

1993

山东省科学技术进步二等奖

 

社会工作

时间

所在机构

担任职务

2017

Topological Methods in Nonlinear Analysis

编委

2016

Analysis in Theory and Applications

编委

2015

Journal of Mathematical Study

编委

2015

数学进展

编委

2010

纯粹数学与应用数学

编委

1997

应用泛函分析学报

编委