刘春根
刘春根，生于1966年，江苏人，南京大学教授[1]，主要研究非线性哈密顿系统; 非线性常微分方程; 非线性偏微分方程边值问题 ; 辛几何与辛拓扑 ; Riemann流形与Finsler流形闭测地线的多重性;奇异积分方程
| 刘春根 | |
|---|---|
|
南京大学教授 | |
| 出生 | 1966年 |
| 国籍 | 中国 |
| 职业 | 教育科研工作者 |
目录
大学教授
个人简介
刘春根博士, 生于1966年，1983年毕业于江苏省海安中学，1987年毕业于苏州大学，获学士学位，1992年在华东理工大学获硕士学位， 1996年获南京大学物理化学博士学位。现为南京大学教授。
主研方向
刘春根博士主要从事大尺度共轭体系的多体半经验算法，以及可运用于准二维共轭体系的密度矩阵重整化群(DMRG)的新型计算方法的研究。
在研项目
大分子共轭体系（从分子到固体）的重整化群计算研究 [项目负责人]（2003.1-2005.12）国家自然科学基金面上项目 共轭分子多体理论方法及光电磁性研究 [主要参与人]（2001-2003）国家自然科学基金项目
南开大学教授
刘春根 男 南开大学数学科学学院教授 博士生导师[2]
研究方向：
非线性哈密顿系统; 非线性常微分方程; 非线性偏微分方程边值问题 ; 辛几何与辛拓扑 ; Riemann流形与Finsler流形闭测地线的多重性;奇异积分方程
社会兼职：
发表文章及著作：
1.刘春根，Douglis 意义下超复函数组的 Riemann 边值问题，南开大学学报，3(1993)34-39。
2.刘春根，具有超复函数的 Cauchy 核的奇异积分方程组，南开大学学报，28(2) (1995)30- 34。
3.Chun-gen Liu, Two-dimensional singular integral equations of the hypercomplex functions, Acta Mathe, Scientia, 16(1) (1996)44-50.
4.C. Liu， Singular integral equations in Douglis Algebra, Complex variables, 29（1996）119-126.
5.Chun-gen Liu, Iteration formula for the ω index with applications. PROGRESS IN NONLINEAR ANALYSIS, Proceedings of the Second International Conference on Nonlinear Analysis at Nankai Institute of Mathematics, Editors: Kung-Ching Chang and Yiming Long, World Scientific, 257-270.
6.Chun-gen Liu， Iteration theory of Maslov-type index and its applications .Proceedings of the workshop on "Morse Theory, Minimax theory and Their applications to Nonlinear Differential Equations". International Press. Ed.:H. Brezis, J. Q. Liu, S. J. Li and H. Rabinowitz.
7.刘春根, 龙以明， Maslov 型迭代指标的一个最佳增长估计，科学通报，42 （21）（1997）2275-2278。
8.C. Liu and Y. Long， An Optimal estimate of Maslov-type index, Chinese Sci. Bull, .43（1998）1063-1066.
9.C. Liu and Y. Long，Hyperbolic characteristics on star-shaped hypersurfaces, Ann. I.H.P. Ana. Nonlinéaire. 16(6), (1999)725-746.
10.刘春根，Maslov型指标与ω指标的单调性，南开大学学报，32(1) (1999)32-38
11.C. Liu，The stability of subharmonic solutions for Hamiltonian systems. Journal of Mathematical Analysis and Applications.240(1999)491-504.
12.C. Liu，Subharmonic solutions of Hamiltonian systems,Nonlinear analysis, 42(2000)185-198.
13.C. Liu and Y. Long， Iteration inequalities of Maslov-type index theory with applications. Journal of Differential Equations . 165(2000)355-376.
14.C. Liu, The stability of the periodic solutions of second order Hamiltonian systems. Chin. Ann. of Math. 21B:2(2000),225-232.
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15.Liu Chun-gen， Eigenvalue problem of Hamiltonian systems, Acta Sci. Natur. Uni. Nankai， 34(1), (2001)65-69.
16.刘春根, 次二次 HAMILTON 系统的对偶 MORSE指标及其闭特征的稳定性. 数学学报, 44(6)(2001)1073- 1088.
17.Chun-gen Liu, Yiming Long and Chaofeng Zhu, Multiplicity of closed characteristics on symmetric convex hypersurfaces. Math. Ann，323(2002)201-215。
18.Chun-gen Liu & Yiming Long, Iterated index formulae for closed geodesics with applications, Science in China，45 (1) (2002)9-28.
19.Liu Chungen, The multiplicity of closed geodesics on some compact simply connected manifolds, Acta Sci. Natur. Uni. Nankai, 37(1) (2004) 33-38
20.Chun-gen Liu, The relation of the Morse index of closed geodesics with the Maslov-type index of symplectic paths, Acta Mathematica Sinica( English Series), 21(2), 2005, 237-248.
21.Chun-Gen Liu, Cup-length estimate for Lagrangian intersections. Journal of Differential Equations 209(2005)57-76.
22.Liu Chungen, A note on the monotonicity of Maslov-type index of linear Hamiltonian systems with applications, Proceedings of the Royal Society of Edinburgh, 135A, 1263-1277, 2005.
23.Liu Chungen, Maslov $P$-index theory for a symplectic path with applications, Chinese Ann. Math. 27B(4), 441-458, 2006.
24.Liu Chungen, The Morse theory and the maslov-type index theory, Bulletin of the Institute of Mathematics, Academia Sinica(New Series), Vol. 1(2006), No. 3, pp. 341-395.
25.Chun-gen Liu, Maslov-type index theory for symplectic paths with Lagrangian boundary conditions, Advanced Nonlinear Studies, 7(2007), 131-161.
26.Chun-gen Liu， Asymptotically linear Hamiltonian systems with Lagrangian boundary conditions. Pacific J. Math. 232 (2007), no. 1, 233--255.
27.Guo F. and Liu C, Existence of a Lagrangian orbit on star-shaped hypersurfaces, Acta Sci. Natur. Uni. Nankai, 41(4)(2008)84-90.
28.Guo F. and Liu C. Multiplicity of Lagrangian orbits on symmetric star-shaped hypersurfaces. Nonlinear Anal. 69 (2008), no. 4, 1425--1436.
2Nontrivial solutions of superquadratic Hamiltonian systems with Lagrangian boundary conditions and the L-index theory. Chinese Ann.Math. 29(6)2008, 597-610.
30.田元生,刘春根.一维$p$-Laplacian算子方程三点奇异边值问题单调正解的多重性.应用数学学报,2008,31(4):635-641.
31.田元生,刘春根.三阶$p$-Laplacian方程三点奇异边值问题三个正解的存在性.应用数学学报,2008,31(6):1118-1127.
32.Guo F. and Liu C，Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces. J. Math.Anal.Appl. 353(2009)88-98.
33 The existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions, Acta Mathematica Scientia, 2009, 29B(2) 313-326.
3 The Existence of Nontrivial Solutions of Hamiltonian Systems with Lagrangian Boundary Conditions and the L-index Theory, Acta Sci. Natur. Uni. Nankai，42(6)(2009), 48-56.
35.田元生,刘春根. 三阶$p$-Laplacian方程三点奇异边值问题正解的存在性, Chinese J. Engin. Math., 26(3)(2009), 519-527.
36.Y. Tian and C. Liu, Multiplicity of positive solutions to M-point boundary value problem of second order impulsive differential equations, Acta Math. Appl. Sinica(English Series), 26(1)(2010)145-158.
37.C. Liu, Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems, Discrete and Continuous Dynamical Systems,27(1)(2010)337 -355
38.Q. Zhang, C. Liu, Infinitely many homoclinic solutions for second order Hamiltonian systems, Nonlinear Analysis: Theory, Methods & Applications,72(2)(2010)894-903.
39.田元生，刘春根，带p-Laplace算子三点奇异边值问题对称正解的存在性，数学物理学报 2010, 30A(3):784-792.
40.田元生，刘春根，一维p拉普拉斯四点边值问题拟对称正解的多重性，系统科学与数学（J. Sys. Sci & Math. Scis），30(3)(2010,3), 349-357.
41.C.Liu and D.Zhang, Brake orbits in bounded convex symmetric domains, Progress in variational methods, Editors: C. Liu and Y.Long, Nankai Pure, Applied Math. and Theor. Phys., vol. 7, 2010, 71-89.
42.Li Chong & LIU ChunGen， Brake subharmonic solutions of first order Hamiltonian systems，SCIENCE CHINA (Mathematics ) , 2010 , Vol. 53 No. 10: 2719-2732 doi: 10.1007/s11425-010-4105-5.
43. Liu C, Wang Q. and Lin X., An index theory for symplectic paths associated with two Lagrangian subspaces with applications. Nonlinearity. 24(2011)43-70.doi:10.1088/0951-7715/24/1/002.
44.Liu C. and Wang Q. Some abstract critical point theorem for self-adjoint operator equations. Chin. Ann. Math. 32B(1), 2011, 1-14.
45.Liu C. and Zhang Q. Existence and Multiplicity of Homoclinic Solutions for the Second Order Hamiltonian systems, International Mathematical Forum, Vol. 6, 2011, no. 4, 159 - 176.
46.Liu. C and Zheng. Y. Linking Solutions for $p$-Laplace Equations with Nonlinear Boundary Conditions and Indefinite Weight, Calc. Var. Partial Differential Equations 41(2011), 261-284. DOI 10.1007
47.Liu. C and Zheng. Y. Existence of nontrivial solutions for p-Laplacian equations in RN Journal of Mathematical Analysis and Applications Vol. 380(2), 2011, 669-679.
48.Zhang Q. and Liu C. Infinitely many periodic solutions for second order Hamiltonian systems.Journal of Differential Equations, 251(2011), 816-833.