刘兆理，男，1963年9月出生，即墨区人，1987年7月参加工作，1993年5月加入中国民主建国会。博士毕业于山东大学，首都师范大学数学科学学院学位委员会主任、教授、博士生导师，非线性分析专家，教育部长江学者特聘教授，北京市特聘教授，北京市首批拔尖人才，教育部创新团队的核心成员，国家杰出青年基金获得者。曾获教育部自然科学二等奖。
学术成就
刘兆理教授长期从事临界点理论及其应用研究，系统地发展了下降流不变集方法，率先将这一新方法成功地应用于非线性椭圆型微分方程理论，在解的存在性、解的个数、变号解的个数、变号解nodal域的个数等方面获得了一批新结果，解决了多个疑难问题。出版专著一部，在Adv. 数学, Comm. Math. Phy., J. Fun.Anal.，Math. Zeit. JDE., Ann. l'Inst. H. Poincaré-Anal. non Linéaire，Comm. PDE等SCI核心期刊上发表学术论文多篇，其研究成果已被他人引用200多次，国际上有多位数学家，包括多位科学院院士，在他们的工作中采用刘兆理教授的研究方法，并称刘兆理教授的工作是开创性工作。
首都师范大学数学科学学院刘兆理教授“临界点理论中若干前沿问题研究”课题获得国家杰出青年科学基金，实现了首都师范大学在此方面零的突破。
首都师范大学数学科学学院刘兆理教授以首都师范大学为第一完成单位申报并获得了教育部高校科学技术奖自然科学二等奖，实现了首都师范大学国家级奖零的突破。
获奖记录
主要论著
Positive solutions of a nonlinear Schrödinger system with nonconstant potentials Haidong Liu · Zhaoli Liu
Existence and uniqueness of positive solutions of nonlinear Schrödinger systems Haidong Liu · Zhaoli Liu · Jinyong Chang
Infinitely many solutions of p-sublinear p-Laplacian 方程 Yongtao Jing · Zhaoli Liu
Multi-bump solutions and multi-tower solutions for equations on $/mathbb R^N$ (with Lishan Lin) Journal of Functional Analysis, to appear.
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.
Multi-bump solutions for a semilinear Schroedinger equation (with Lishan Lin and Shaowei Chen) Indiana University 数学 Journal, to appear.
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.
A twist condition and periodic solutions of Hamiltonian systems (with Jiabao Su and Zhi-Qiang Wang) Advances in 数学, 218(2008), 1895-1913.
multiple bound states of nonlinear Schrodinger systems (with Zhi-Qiang Wang) Communications in Mathematical Physics, 282(2008), 721-731.
Nodal solutions of a perturbed elliptic problem (with Yi Li and Chun-Shan Zhao) Topological Methods in Nonlinear Analysis, 32(2008), 49-68.
On the Fucik spectrum (with Chong Li, Shujie Li, and Jianzhong pan) Journal of Differential Equations, 244(2008), 2498-2528.
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.
Sign-changing solutions of nonlinear elliptic equations (with Zhi-Qiang Wang) Frontiers of 数学 in China, 3(2008), 221-238
Bounded 共振 problem for semilinear elliptic equations (with Jia-Bao Su) Discrete and Continuous Dynamical Systems, 19(2007), 431-445
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
multiple solutions of nonlinear Schroedinger equations via flow invariance and 海象 theory (with Zhi-Qiang Wang and Tobias Weth) Proceedings of the Royal Society of 爱丁堡, 136A(2006), 945-969
Compactness results for Schroedinger equations with asymptotically linear terms (with Jia-Bao Su and Tobias Weth) Journal of Differential Equations, 231(2006) 501–512.
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.
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.
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.
Multi-bump type nodal solutions having a prescribed number of nodal domains: II (with Zhi-Qiang Wang) Annales de l'Institut Henri Poincare-数学分析 Non Lineaire, 22(2005), 609-631.
An elliptic problem with jumping nonlinearities (with Jing-Xian Sun) Nonlinear Analysis, Theory, Method and Application, 63(2005), 1070-1082.
Schroedinger equations with concave and convex nonlinearities (with Zhi-Qiang Wang) Zeitschrift fur Angewandte Mathematik und Physik, 56(2005), 609-629.
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.
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.
multiple sign changing solutions of a quasilinear elliptic eigenvalue problem involving the $p$-Laplacian (with Thomas Bartsch) Communications in Contemporary 数学, 6(2004), 245-258.
On a superlinear elliptic $p$-Laplacian equation (with Thomas Bartsch) Journal of Differential Equations, 198(2004), 149-175.
Sign-changing solutions of superlinear Schr/"odinger equations (with Thomas Bartsch and Tobias Weth) Communications in Partial Differential Equations, 29(2004), 25-42.
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.
On the Ambrosetti-Rabinowitz superlinear condition (with Zhi-Qiang Wang) Advanced Nonlinear Studies, 4(2004), 563-574.
Nontrivial solutions for perturbed $p$-Laplacian on ${/cal R}^N$ (with Jia-Bao Su) Mathematische Nachrichten,248-249(2003), 190-199.
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.
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.
Number of invariant sets of descending flow with applications in critical 小数点 theory (with Jing-Xian Sun) in: 海象 Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations-Lectures at Morningside Center of 数学, ed. H. Brezis, sj Li, J.Q. Liu, and P.H. Rabinowitz, International Press, New York, 2003, pp 139--156.
Multiplicity of solutions of semilinear elliptic boundary value problems with jumping nonlinearities at zero Nonlinear Analysis, Theory, Method and Application, 48(2002), 1051-1063.
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.
Positive solutions of a class of nonlinear elliptic eigenvalue problems Mathematische Zeitschrift, 242(2002), 663-686.
Perturbations of symmetric eigenvalue problems (with Yong-Qing Li) Applied 数学 Letters, 15(2002), 903-906.
Perturbations from symmetric elliptic boundary value problems (with Shu-Jie Li) Journal of Differential Equations, 185(2002), 271-280.
A class of two-小数点 boundary value problems (with Xue-Mei Zhang) Journal of Mathematical Analysis and Applications, 254(2001), 599-617.
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.
Properties of positive solutions of a nonlinear eigenvalue problem (with Yong-Qing Li) Zeitschrift fur Angewandte Mathematik und Physik, 52(2001), 433-447.
Exact number of solutions of a class of two-小数点 boundary value problems involving concave and convex nonlinearities Nonlinear Analysis, Theory, Method and Application, 46(2001), 181-197.
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.
Solutions of an elliptic eigenvalue problem involving subcritical and critical exponents (with Yong-Qing Li) Communications in Partial Differential Equations, 26(2001), 2227-2248.
On the existence of positive solutions of a elliptic boundary value problem (with Fu-Yi Li) Chinese Annals of 数学, 21B(2000), 499-510.
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.
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.
Positive solutions of superlinear elliptic equations Journal of Functional Analysis, 167(1999), 370-398.
multiple positive solutions of some nonlinear operator equations and applications (with Fu-Yi Li) Acta Mathematica Sinica, 41(1998), 97-102 (in Chinese).
Multiple positive solutions of nonlinear two-小数点 boundary value problems (with Fu-Yi Li) Journal of Mathematical Analysis and Applications, 203(1996), 610-625.
Periodic solutions for nonlinear $n$th-order ordinary differential equations Journal of Mathematical Analysis and Applications, 204(1996), 46-64.
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).
Calculus of variations and super- and sub-solutions in reversed order (with Jing-Xian Sun) Acta Mathematica Sinica, 37(1994), 512-514, (in Chinese).
Chong Li, Shujie Li, Zhaoli Liu, Bifurcation surfaces stemming from the Fucik spectrum，Journal of Functional Analysis, Vo.263, Issue 12(2012), 4059-4080.
科研项目
2006年1月至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1月至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
学术报告
• 嘉兴学院
2011年11月3日上午，首都师范大学数学科学学院数学系主任、博士生导师、教育部长江学者特聘教授、国家杰出青年基金获得者、北京市特聘教授刘兆理教授应邀到数信学院讲学，为数学系部分教师和研究生作了一场精彩的学术报告。刘教授的报告题为《Multibump and multitower solutions of nonlinear Schrodinger equations》，主要介绍了椭圆型偏微分方程的多包解和多塔解的存在性，认为这类解在相应的极限方程中是不存在的。
刘兆理教授多年来从事临界点理论及其应用的研究，在变分方法和非线性偏微分方程方面做出了突出的研究成果，在国际重要学术期刊上发表论文60多篇，其研究成果被国际上许多著名数学家引用。
报告结束后，刘教授和部分年轻教师进行了座谈交流，刘教授热情回答了大家的提问。
2013年11月23日下午，教育部长江学者特聘教授，国家杰出青年基金获得者，首都师范大学系主任刘兆理教授应邀来我校做了题目为“On Clark's theorem and its applications to partially sublinear problems”的报告。
我校葛翔宇教授，周爽博士，魏娜博士等青年教师及数量经济学专业研究生参加了本次学术活动。刘兆理教授长期从事临界点理论及其应用的研究，发展了下降流不变集方法，并将这一方法率先成功地应用于非线性微分方程理论的研究中，为非线性泛函分析的发展及其应用做出了特殊贡献。本次报告中，刘教授用简单易懂的方式介绍了下降流方法，为大家提供了求解临界点新工具，在座师生受益匪浅。
本次学术活动受到学校“研究生创新教育计划”专项经费资助。
2016年6月4日-5日，知名学者 刘兆理教授应邀来曲阜师范大学数学科学学院作学术报告，数学院众多教师和研究生们聆听了报告会，报告由数学科学院院长孟凡伟主持。
刘兆理教授重点讲述了其本人关于著名的Clarke定理的推广和改进，展示了下降流不变集方法的独特的应用价值。此次学术报告活动极大开阔了师生们的学术视野，提高了对非线性分析理论及其应用的了解。
教学工作
授课记录
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
执教业绩
首都师范大学数学科学学院刘兆理教授指导的林丽珊博士的论文《某些非线性椭圆型方程的多重正解》入选2010年北京市优秀博士学位论文。至此，首都师范大学已有六名博士获得北京市优秀博士学位论文奖。
社会工作
学报编委
1997年至今 应用泛函分析学报 编委
政协委员
经中共海淀区委常委会研究，拟提名陈鹏、雷达、刘兆理、汪龙麟、吴敏华、颜忠诚等6名同志为政协北京市海淀区第九届委员会委员人选。
作为大学教授，刘兆理对高等教育的发展十分关注。他正在深入研究关于高等教育的教学、科研，以及相关评价系统的体系。他认为，这些都需要进一步改革，才能利于高等教育的发展。
作为政协委员，刘兆理非常关注居民生活的环境状况。他提及一个现象，即城市生活中，很多居民都需要装修房子，以一个社区为例，从第一户开始装修到最后一户装修完毕，每家都会产生3-4个月的噪音和很多装修垃圾，而且每户单独装修既不经济又不低碳，还牵涉个人精力。针对这一现象，刘兆理希望能够深入调研后做一个提案，呼吁以城市为单位进行房屋装修改造，既节省大量人力物力，也利于环境保护。
参考资料