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: 

 

 

 

 

教学活动

开课时间 课程名称 授课对象 课件
2008年秋季 变分方法与非线性偏微分方程 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

论文题目(书名) 期刊(出版社) 下载
51. Multi-bump solutions and multi-tower solutions for equations on $/mathbb R^N$ (with Lishan Lin) Journal of Functional Analysis, to appear. 下载
50. Solutions of elliptic problems with nonlinearities of linear growth (with Jiabao Su and Zhi-Qiang Wang) Calculus of Variations and Partial Differential Equations, to appear. 下载
49. Multi-bump solutions for a semilinear Schroedinger equation (with Lishan Lin and Shaowei Chen) Indiana University Mathematics Journal, to appear. 下载
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. 下载
47. A twist condition and periodic solutions of Hamiltonian systems (with Jiabao Su and Zhi-Qiang Wang) Advances in Mathematics, 218(2008), 1895-1913. 下载
46. Multiple bound states of nonlinear Schrodinger systems (with Zhi-Qiang Wang) Communications in Mathematical Physics, 282(2008), 721-731. 下载
45. Nodal solutions of a perturbed elliptic problem (with Yi Li and Chun-Shan Zhao) Topological Methods in Nonlinear Analysis, 32(2008), 49-68. 下载
44. On the Fucik spectrum (with Chong Li, Shujie Li, and Jianzhong Pan) Journal of Differential Equations, 244(2008), 2498-2528. 下载
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. 下载
42. Sign-changing solutions of nonlinear elliptic equations (with Zhi-Qiang Wang) Frontiers of Mathematics in China, 3(2008), 221-238 下载
41. Bounded resonance problem for semilinear elliptic equations (with Jia-Bao Su) Discrete and Continuous Dynamical Systems, 19(2007), 431-445 下载
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 下载
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 下载
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. 下载
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. 下载
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. 下载
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. 下载
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. 下载
33. An elliptic problem with jumping nonlinearities (with Jing-Xian Sun) Nonlinear Analysis, Theory, Method and Application, 63(2005), 1070-1082. 下载
32. Schroedinger equations with concave and convex nonlinearities (with Zhi-Qiang Wang) Zeitschrift fur Angewandte Mathematik und Physik, 56(2005), 609-629. 下载
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. 下载
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. 下载
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. 下载
28. On a superlinear elliptic $p$-Laplacian equation (with Thomas Bartsch) Journal of Differential Equations, 198(2004), 149-175. 下载
27. Sign-changing solutions of superlinear Schr/"odinger equations (with Thomas Bartsch and Tobias Weth) Communications in Partial Differential Equations, 29(2004), 25-42. 下载
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. 下载
25. On the Ambrosetti-Rabinowitz superlinear condition (with Zhi-Qiang Wang) Advanced Nonlinear Studies, 4(2004), 563-574. 下载
24. Nontrivial solutions for perturbed $p$-Laplacian on ${/cal R}^N$ (with Jia-Bao Su) Mathematische Nachrichten,248-249(2003), 190-199. 下载
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. 下载
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. 下载
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. 下载
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. 下载
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. 下载
18. Positive solutions of a class of nonlinear elliptic eigenvalue problems Mathematische Zeitschrift, 242(2002), 663-686. 下载
17. Perturbations of symmetric eigenvalue problems (with Yong-Qing Li) Applied Mathematics Letters, 15(2002), 903-906. 下载
16. Perturbations from symmetric elliptic boundary value problems (with Shu-Jie Li) Journal of Differential Equations, 185(2002), 271-280. 下载
15. A class of two-point boundary value problems (with Xue-Mei Zhang) Journal of Mathematical Analysis and Applications, 254(2001), 599-617. 下载
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. 下载
13. Properties of positive solutions of a nonlinear eigenvalue problem (with Yong-Qing Li) Zeitschrift fur Angewandte Mathematik und Physik, 52(2001), 433-447. 下载
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. 下载
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. 下载
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. 下载
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. 下载
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. 下载
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. 下载
6. Positive solutions of superlinear elliptic equations Journal of Functional Analysis, 167(1999), 370-398. 下载
5. Multiple positive solutions of some nonlinear operator equations and applications (with Fu-Yi Li) Acta Mathematica Sinica, 41(1998), 97-102 (in Chinese). 下载
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. 下载
3. Periodic solutions for nonlinear $n$th-order ordinary differential equations Journal of Mathematical Analysis and Applications, 204(1996), 46-64. 下载
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). 下载
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). 下载

 

 

 

科研项目

开始时间 截止时间 项目名称 资金来源
2006年01月 2008年12月 临界点理论中几个重要问题 国家自然科学基金
2005年01月 2005年12月 变分方法与非线性椭圆型方程的变号解 国家自然科学基金

 

所获奖励

获奖时间 所获奖励
2008年01月 教育部高等学校自然科学奖二等奖
2002年12月 山东省自然科学奖二等奖
1998年12月 山东省科学技术进步奖一等奖
1993年12月 山东省科学技术进步奖二等奖

 

社会工作

时间 所在机构 担任职务
1997年-- 应用泛函分析学报 编委