劉兆理

2012年 首都勞動獎章

2011年 北京市教育工會教育先鋒教書育人標兵

2011年 國務院特殊津貼

2010年 北京市優秀博士學位論文指導教師

2009年 教育部“獎勵計劃”長江學者特聘教授

2008年 新世紀百千萬人才工程北京市市級人選

2008年 國家傑出青年科學基金

2008年 教育部高校自然科學二等獎

2006年 北京市特聘教授

2002年 山東省自然科學二等獎

1998年 山東省科學技術進步一等獎

1993年 山東省科學技術進步二等獎 ^[5] 

1. Quasilinear Schrödinger equations involving singular potentials (with Yongtao Jing and Haidong Liu), Nonlinearity, 35 (2022), 1810–1856.

2. Ground states of a system of three Schrödinger equations (with Chen Xinyan and Liu Haidong), Pure and Applied Mathematics, 37 (2021), 1-24.

3. Normalized solutions for a class of nonlinear Choquard equations (with Thomas Bartsch and Yanyan Liu), SN Partial Differ. Equ. Appl. (2020) 1:34, DOI: 10.1007/s42985-020-00036-w.

4. Transition between nonlinear and linear eigenvalueproblems, (with Guosheng Jiang and Yongjie Liu), J. Differential Equations, 269 (2020), 10919–10936.

5. A coupled Schrödinger system with critical exponent (with Haidong Liu), Calculus of Variations and Partial Differential Equations, 2020, DOI: 10.1007/s00526-020-01803-8.

6. Vector solutions with prescribed component-wise nodes for a schrodinger system (with Zhi-Qiang Wang), Analysis in Theory and Applications, 35 (2019), 288-311.

7. Multiple positive solutions of elliptic systems in exterior domains (with Haidong Liu), Communications in Contemporary Mathematics, 2018, DOI: 10.1142/S0219199717500638.

8. 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.

9. 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.

10. 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.

11. 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.

12. Positive solutions of a nonlinear Schrodinger system with nonconstant potentials (with Haidong Liu), Discrete and Continuous Dynamical Systems-A, 36 (2016), 1431-1464.

13. Elliptic systems with a partially sublinear local term (with Yongtao Jing), Journal of Mathematical Study, 48 (2015), 290-305.

14. 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.

15. Infinitely many solutions of p-sublinear p-Laplacian equations (with Yongtao Jing), Journal of Mathematical Analysis and Applications, 429 (2015), 1240-1257.

16. 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.

17. Ground states of a nonlinear Schrodinger system with nonconstant potentials (with Haidong Liu), Science China: Mathematics, 58 (2015), 257-278.

18. Perturbed elliptic equations with oscillatory nonlinearities (with Zuji Guo), Discrete and Continuous Dynamical Systems-A, 32 (2012), 3567-3585.

19. Bifurcation surfaces stemming from the Fucik spectrum (with Chong Li and Shujie Li), Journal of Functional Analysis, 263 (2012), 4059-4080.

20. Radial solutions of a supercritical elliptic equation with Hardy potential (with Zuji Guo), Advanced Nonlinear Studies, 12 (2012), 49-66.

21. Multi-bubble solutions for equations of CKN type (with Lishan Lin), Communications in Contemporary Mathematics, 13 (2011), 945-968.

22. Exact number of solutions of a prescribed mean curvature equation (with Weisheng Li), Journal of Mathematical Analysis and Applications, 367 (2010), 486-498

23. Ground states and bound states of a nonlinear Schrodinger system (with Zhi-Qiang Wang), Advanced Nonlinear Studies, 10 (2010), 175-193.

24. Ground states of nonlinear Schrodinger Systems (with Jinyong Chang), Proceedings of the American Mathematical Society, 138 (2010), 687-693.

25. Multi-bump solutions and multi-tower solutions for equations on R^N (with Lishan Lin), Journal of Functional Analysis, 257 (2009), 485-505.

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

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

28. Multi-bump solutions for a semilinear Schrodinger equation (with Lishan Lin and Shaowei Chen), Indiana University Mathematics Journal, 58 (2009), 1659-1689.

29. 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.

30. A twist condition and periodic solutions of Hamiltonian systems (with Jiabao Su and Zhi-Qiang Wang), Advances in Mathematics, 218 (2008), 1895-1913.

31. Multiple bound states of nonlinear Schrodinger systems (with Zhi-Qiang Wang), Communications in Mathematical Physics, 282 (2008), 721-731.

32. Nodal solutions of a perturbed elliptic problem (with Yi Li and Chun-Shan Zhao), Topological Methods in Nonlinear Analysis, 32 (2008), 49-68.

33. On the Fucik spectrum (with Chong Li, Shujie Li, and Jianzhong Pan), Journal of Differential Equations, 244 (2008), 2498-2528.

34. 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.

35. Sign-changing solutions of nonlinear elliptic equations (with Zhi-Qiang Wang), Frontiers of Mathematics in China, 3 (2008), 221-238

36. Bounded resonance problem for semilinear elliptic equations (with Jia-Bao Su), Discrete and Continuous Dynamical Systems, 19 (2007), 431-445

37. 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

38. 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

39. Compactness results for Schroedinger equations with asymptotically linear terms (with Jia-Bao Su and Tobias Weth), Journal of Differential Equations, 231 (2006) 501–512.

40. 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.

41. 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.

42. 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.

43. 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.

44. An elliptic problem with jumping nonlinearities (with Jing-Xian Sun), Nonlinear Analysis, Theory, Method and Application, 63 (2005), 1070-1082.

45. Schroedinger equations with concave and convex nonlinearities (with Zhi-Qiang Wang), Zeitschrift fur Angewandte Mathematik und Physik, 56 (2005), 609-629.

46. 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.

47. 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.

48. 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.

49. On a superlinear elliptic $p$-Laplacian equation (with Thomas Bartsch), Journal of Differential Equations, 198 (2004), 149-175.

50. Sign-changing solutions of superlinear Schrodinger equations (with Thomas Bartsch and Tobias Weth), Communications in Partial Differential Equations, 29 (2004), 25-42.

51. 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.

52. On the Ambrosetti-Rabinowitz superlinear condition (with Zhi-Qiang Wang), Advanced Nonlinear Studies, 4 (2004), 563-574.

53. Nontrivial solutions for perturbed $p$-Laplacian on ${/cal R}^N$ (with Jia-Bao Su), Mathematische Nachrichten, 248-249 (2003), 190-199.

54. 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.

55. 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.

56. 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.

57. Multiplicity of solutions of semilinear elliptic boundary value problems with jumping nonlinearities at zero, Nonlinear Analysis, Theory, Method and Application, 48 (2002), 1051-1063.

58. 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.

59. Positive solutions of a class of nonlinear elliptic eigenvalue problems, Mathematische Zeitschrift, 242 (2002), 663-686.

60. Perturbations of symmetric eigenvalue problems (with Yong-Qing Li), Applied Mathematics Letters, 15 (2002), 903-906.

61. Perturbations from symmetric elliptic boundary value problems (with Shu-Jie Li), Journal of Differential Equations, 185 (2002), 271-280.

62. A class of two-point boundary value problems (with Xue-Mei Zhang), Journal of Mathematical Analysis and Applications, 254 (2001), 599-617.

63. 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.

64. Properties of positive solutions of a nonlinear eigenvalue problem (with Yong-Qing Li), Zeitschrift fur Angewandte Mathematik und Physik, 52 (2001), 433-447.

65. 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.

66. 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.

67. Solutions of an elliptic eigenvalue problem involving subcritical and critical exponents (with Yong-Qing Li), Communications in Partial Differential Equations, 26 (2001), 2227-2248.

68. On the existence of positive solutions of a elliptic boundary value problem (with Fu-Yi Li), Chinese Annals of Mathematics, 21B (2000), 499-510.

69. 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.

70. 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.

71. Positive solutions of superlinear elliptic equations, Journal of Functional Analysis, 167 (1999), 370-398.

72. Multiple positive solutions of some nonlinear operator equations and applications (with Fu-Yi Li), Acta Mathematica Sinica, 41 (1998), 97-102 (in Chinese).

73. Multiple positive solutions of nonlinear two-point boundary value problems (with Fu-Yi Li), Journal of Mathematical Analysis and Applications, 203 (1996), 610-625.

74. Periodic solutions for nonlinear nth-order ordinary differential equations, Journal of Mathematical Analysis and Applications, 204 (1996), 46-64.

75. 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).

76. Calculus of variations and super- and sub-solutions in reversed order (with Jing-Xian Sun), Acta Mathematica Sinica, 37 (1994), 512-514, (in Chinese). ^[5] 

2021.1 2025.12 國家自然科學基金重點項目 國家自然科學基金委

2017.1 2020.12 國家自然科學基金面上項目 國家自然科學基金委

2014.1 2018.12 國家自然科學基金重點項目子項目 國家自然科學基金委

2013.1 2016.12 國家自然科學基金面上項目 國家自然科學基金委

2010.1 2012.12 北京市高等學校“高層次人才”項目 北京市教委

2009.1 2013.12 國家自然科學基金重點項目子項目 國家自然科學基金委

2009.1 2012.12 國家傑出青年科學基金 國家自然科學基金委

2006.1 2006.12 人事部留學人員科技活動擇優資助項目 國家人事部

2006.1 2006.12 教育部留學回國基金 國家教育部

2006.1 2008.12 北京市教委重點項目 北京市教委

2005.1 2007.12 北京市高等學校“創新拔尖人才”項目 北京市教委

2005.1 2008.12 國家自然科學基金面上項目 國家自然科學基金委

2004.1 2004.12 國家自然科學基金專項基金項目 國家自然科學基金委 ^[5] 

2022年春季 常微分方程/非線性泛函分析 本科生/研究生

2021年春季 變分方法及應用 研究生

2021年春季 常微分方程/非線性泛函分析 本科生/研究生

2020年秋季 泛函分析 研究生

2019年秋季 泛函分析 研究生

2019年春季 非線性分析方法 研究生

2018年秋季 高等分析 本科生

2018年秋季 現代變分方法 研究生

2018年春季 變分方法與非線性微分方程 研究生

2016年秋季 數學分析 本科生

2013年秋季 臨界點理論及其應用 研究生

2013年秋季 非線性泛函分析 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 非線性泛函分析 研究生

2012年春季 微分方程中的變分方法 研究生

2011年秋季 變分方法與非線性微分方程 研究生

2011年秋季 臨界點理論及其應用 研究生

2011年秋季 分析選講 本科生

2011年春季 臨界點理論及其應用 研究生

2010年秋季 泛函分析 研究生

2010年春季 非線性泛函分析 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 變分方法與非線性微分方程 研究生

2008年秋季 變分方法與非線性微分方程 研究生

2008年春季 非線性泛函分析 研究生

2007年春季 非線性泛函分析 研究生

2006年秋季 泛函分析 研究生

2006年春季 非線性分析方法 研究生

2005年春季 非線性泛函分析 研究生 ^[5]