劉春根[南開大學數學科學學院教授]

劉春根，男，現為南開大學數學科學學院教授，博士生導師。

研究方向

非線性哈密頓系統、非線性常微分方程、非線性偏微分方程邊值問題、辛幾何與辛拓撲、Riemann流形與Finsler流形閉測地線的多重性、奇異積分方程。

文章著作

1．劉春根，Douglis 意義下超複函數組的 Riemann 邊值問題，南開大學學報，3(1993)34-39。

2．劉春根，具有超複函數的 Cauchy 核的奇異積分方程組，南開大學學報，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．劉春根，龍以明， Maslov 型疊代指標的一個最佳增長估計，科學通報，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．劉春根，Maslov型指標與ω指標的單調性，南開大學學報，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.

15．Liu Chun-gen， Eigenvalue problem of Hamiltonian systems, Acta Sci. Natur. Uni. Nankai， 34(1), (2001)65-69.

16．劉春根, 次二次 HAMILTON 系統的對偶 MORSE指標及其閉特徵的穩定性. 數學學報, 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,劉春根.一維$p$-Laplacian運算元方程三點奇異邊值問題單調正解的多重性.套用數學學報,2008,31(4):635-641.

31．田元生,劉春根.三階$p$-Laplacian方程三點奇異邊值問題三個正解的存在性.套用數學學報,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,劉春根. 三階$p$-Laplacian方程三點奇異邊值問題正解的存在性, 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，劉春根，帶p-Laplace運算元三點奇異邊值問題對稱正解的存在性，數學物理學報 2010, 30A(3):784-792.

40．田元生，劉春根，一維p拉普拉斯四點邊值問題擬對稱正解的多重性，系統科學與數學（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.