劉兆理

劉兆理教授長期從事臨界點理論及其應用研究，系統地發展了下降流不變集方法，率先將這一新方法成功地應用於非線性橢圓型微分方程理論，在解的存在性、解的個數、變號解的個數、變號解nodal域的個數等方面獲得了一批新結果，解決了多個疑難問題。出版專著一部，在Adv. Math., Comm. Math. Phy., J. Fun.Anal.，Math. Zeit. JDE., Ann. l'Inst. H. Poincaré-Anal. non Linéaire，Comm. PDE等SCI核心期刊上發表學術論文多篇，其研究成果已被他人引用200多次，國際上有多位數學家，包括多位科學院院士，在他們的工作中採用劉兆理教授的研究方法，並稱劉兆理教授的工作是開創性工作。

首都師範大學數學科學學院劉兆理教授“臨界點理論中若干前沿問題研究”課題獲得國家傑出青年科學基金，實現了首都師範大學在此方面零的突破。

首都師範大學數學科學學院劉兆理教授以首都師範大學為第一完成單位申報並獲得了教育部高校科學技術獎自然科學二等獎，實現了首都師範大學國家級獎零的突破。

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 equation 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 Mathematics 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 Mathematics, 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 Mathematics in China, 3(2008), 221-238

Bounded resonance 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 Morse theory (with Zhi-Qiang Wang and Tobias Weth) Proceedings of the Royal Society of Edinburgh, 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-Analyse 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 Mathematics, 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 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.

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 Mathematics 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-point 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-point 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 Mathematics, 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-point 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.

2006年1月至2008年12月 臨界點理論中幾個重要問題 國家自然科學基金

2005年1月至2005年12月 變分方法與非線性橢圓型方程的變號解 國家自然科學基金

• 嘉興學院

2011年11月3日上午，首都師範大學數學科學學院數學系主任、博士生導師、教育部長江學者特聘教授、國家傑出青年基金獲得者、北京市特聘教授劉兆理教授應邀到數信學院講學，為數學系部分教師和研究生作了一場精彩的學術報告。劉教授的報告題為《Multibump and multitower solutions of nonlinear Schrodinger equations》，主要介紹了橢圓型偏微分方程的多包解和多塔解的存在性，認為這類解在相應的極限方程中是不存在的。

劉兆理教授多年來從事臨界點理論及其應用的研究，在變分方法和非線性偏微分方程方面做出了突出的研究成果，在國際重要學術期刊上發表論文60多篇，其研究成果被國際上許多著名數學家引用。

報告結束后，劉教授和部分年輕教師進行了座談交流，劉教授熱情回答了大家的提問。

•中南財經政法大學

2013年11月23日下午，教育部長江學者特聘教授，國家傑出青年基金獲得者，首都師範大學系主任劉兆理教授應邀來我校做了題目為“On Clark's theorem and its applications to partially sublinear problems”的報告。

我校葛翔宇教授，周爽博士，魏娜博士等青年教師及數量經濟學專業研究生參加了本次學術活動。劉兆理教授長期從事臨界點理論及其應用的研究，發展了下降流不變集方法，並將這一方法率先成功地應用於非線性微分方程理論的研究中，為非線性泛函分析的發展及其應用做出了特殊貢獻。本次報告中，劉教授用簡單易懂的方式介紹了下降流方法，為大家提供了求解臨界點新工具，在座師生受益匪淺。

本次學術活動受到學校“研究生創新教育計劃”專項經費資助。

•曲阜師範大學

2016年6月4日-5日，知名學者 劉兆理教授應邀來曲阜師範大學數學科學學院作學術報告，數學院眾多教師和研究生們聆聽了報告會，報告由數學科學院院長孟凡偉主持。

劉兆理教授重點講述了其本人關於著名的Clarke定理的推廣和改進，展示了下降流不變集方法的獨特的應用價值。此次學術報告活動極大開闊了師生們的學術視野，提高了對非線性分析理論及其應用的了解。

2008年秋季 變分方法與非線性偏微分方程 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

首都師範大學數學科學學院劉兆理教授指導的林麗珊博士的論文《某些非線性橢圓型方程的多重正解》入選2010年北京市優秀博士學位論文。至此，首都師範大學已有六名博士獲得北京市優秀博士學位論文獎。

1997年至今 應用泛函分析學報 編委

經中共海淀區委常委會研究，擬提名陳鵬、雷達、劉兆理、汪龍麟、吳敏華、顏忠誠等6名同志為政協北京市海淀區第九屆委員會委員人選。

作為大學教授，劉兆理對高等教育的發展十分關注。他正在深入研究關於高等教育的教學、科研，以及相關評價系統的體系。他認為，這些都需要進一步改革，才能利於高等教育的發展。

作為政協委員，劉兆理非常關注居民生活的環境狀況。他提及一個現象，即城市生活中，很多居民都需要裝修房子，以一個社區為例，從第一戶開始裝修到最後一戶裝修完畢，每家都會產生3-4個月的噪音和很多裝修垃圾，而且每戶單獨裝修既不經濟又不低碳，還牽涉個人精力。針對這一現象，劉兆理希望能夠深入調研后做一個提案，呼籲以城市為單位進行房屋裝修改造，既節省大量人力物力，也利於環境保護。