刘春根

作者: 时间:2018-09-19 点击数:

1、 基本信息

 

刘春根教授

 

研究领域:非线性分析,特别是非线性哈密顿系统及相关问题,辛几何与辛拓扑,非线性微分方程(用变分法),黎曼几何和芬斯勒几何中的测地线问题。

 

办公地点:行政西楼前座443。

 

电子邮箱,liucg@nankai.edu.cn

 

  

二、个人简介

1962年出生,湖南省耒阳市人. 1996年破格晋升为副教授,1999年破格晋升为教授,2001年任博士生导师。2017年------,广州大学数学与信息学院教授,博士生导师。

 

三、教育背景

1978年-1981年,在湖南郴州师专(现湘南学院)数学系学习

1984年至1986年在湖南教育学院脱产进修大学本科课程。

1989年-1992年,在北京师范大学数学系攻读硕士学位。

1995年月-1998年在南开数学所攻读博士学位。

2001年8月-2002年8月,在德国莱比锡Max-Planck数学所做博士后研究

 

四、职业经历

1.学术工作经历: 1992年-2017年,在南开大学数学学院任教。

2.海外工作经历: 2001年8月-2002年8月,在德国莱比锡Max-Planck数学所做博士后研究工作。

五、教授课程:大学本科生的“微分方程定性理论”,研究生的“微分流形”,“数学前沿讲座”。

 

六、科研服务

近年主持的研究项目:

国家自然科学基金:“哈密顿系统与微分方程中一些问题的研究”,批准号:11471170,起止年限:2015.01-2018.12

国家自然科学基金重大项目:“哈密顿系统的周期轨道和辛映射的不动点研究“,批准号:11790271,2018.01-2021.12.

广东省基础与应用基础研究基金项目:“有穷维与无穷维哈密顿系统”,批准号:11471170,起止年限:2019.10.01-2022.09.30.

 

七、研究成果

获奖及荣誉

1998年获中国数学会钟家庆数学奖

2000年获教育部全国优秀博士论文奖

2003年获教育部自然科学一等奖

2004年获国家自然科学二等奖

2014年获国务院政府津贴。

 

近5年论著目录:

Index theory in nonlinear analysis. Springer & Science Press. 2019.

 

近期发表的期刊文章:

1. An index theory for symplectic paths associated with two Lagrangian subspaces with applications. Nonlinearity. 24(1)(2011)43-70. (with Wang Q. and Lin X.) .

2. Some abstract critical point theorem for self-adjoint operator equations. Chin. Ann. Math. 32B(1), 2011, 1-14. (with Wang Q.).

3. Existence and Multiplicity of Homoclinic Solutions for the Second Order Hamiltonian systems, International Mathematical Forum, Vol. 6, 2011, no. 4, 159 – 176. (with Zhang Q.).

4. Liu. C and Linking Solutions for $p$-Laplace Equations with Nonlinear Boundary Conditions and Indefinite Weight, Calc. Var. Partial Differential Equations 41(no.1-2)(2011), 261-284. (with Zheng. Y.).

5. Existence of nontrivial solutions for p-Laplacian equations in RN Journal of Mathematical Analysis and Applications Vol. 380(2), 2011, 669-679. (with Zheng. Y.).

6. Infinitely many periodic solutions for second order Hamiltonian systems. Journal of Differential Equations, 251(no.4-5)(2011), 816-833. (with Zhang Q.).

7. Multiple positive solutions to a nonhomogeneous boundary value problem for a class of third-order $p$p-Laplacian equations. (Chinese) Adv. Math. (China) 40(1) (2011). 71–78. (with Tian Y.).

8. Symmetrical Symplectic Capacity with Applications, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,Volume 32, Number 6, 2012, pp. 2253-2270 (with Wang Q.).

9. Periodic solutions of asymptotically linear delay differential systems via Hamiltonian systems, J. Differential Equations,252 (no.10)(2012) 5712–5734.

10. On soliton solutions of a class of Schrodinger-KdV system, to appear in Proceedings of the American Mathematical Society. (with Zheng. Y.).

11. Nontrivial solutions for asmptotically linear Hamiltonian systems with Lagrangian boundary conditions . Acta Matematica Scientia, 2012,32B(4):1545-1558. (with Zhang Q.).

12. Multiple solutions for a class of semilinear elliptic equations with general potentials, Nonlinear Analysis, 75 (no.14)(2012) 5473–5481. (with Zhang Q.).

13. Multiplicity of brake orbits on compact convex symmetric reversible hypersurfaces in R2n for n≥4. Proc. Lond. Math. Soc. (3) 107 (2013), no. 1, 1–38. (with Zhang D.).

14. Multiple brake orbits on compact convex symmetric reversible hypersurfaces in R^{2n}. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 3, 531–554. (with Zhang D.).

15. Periodic solutions of delay differential systems via Hamiltonian systems. Nonlinear Anal. 102 (2014), 159–167. (with Wang Q.).

16. Iteration theory of L-index and multiplicity of brake orbits. J. Differential Equations 257 (2014), no. 4, 1194–1245. (with Zhang D.).

17. Seifert conjecture in the even convex case. Comm. Pure Appl. Math. 67 (2014), no. 10, 1563–1604. (with Zhang D.).

18. The relative Morse index theory for infinite dimensional Hamiltonian systems with applications. J. Math. Anal. Appl. 427 (2015), no. 1, 17–30. (with Wang Q.).

19. On the steady-state solutions of a nonlinear photonic lattice model,Journal of Mathematical Physics 56, 031501 (2015). (with Ren Q.).

20. On the Lagrangian boundary problem of Hamiltonian systems and Seifert conjecture, Advances in Mathematics(China). 44(2) (2015), 161-169.

21. On soliton solutions for a class of discrete Schr\"{o}dinger systems, Advances in differential equations and control processes, 15(1), 2015, 19-43. (with Zheng. Y.).

22. Iteration inequalities of the Maslov P-index theory with applications. Nonlinear Anal. 127 (2015), 215–234. (with Tang S.).

23. Maslov (P;\omega)-Index Theory for Symplectic Paths. Advanced Nonlinear Studies 15 (2015), 963–990. (with Tang S.).

24. A new index theory for linear self-adjoint operator equations and its applications. J. Differential Equations 260 (2016) 3749–3784. (with Wang Q.).

25. Existence results for the fractional Nirenberg problem, Journal of Functional Analysis, 270 (2016) 4043–4086. (with Chen Y. & Zheng Y.).

26. Ground state solutions for non-autonomous fractional Choquard equations, Nonlinearity 29 (2016) 1827–1842. (with Chen Y.).

27. Subharmonic Solutions and Minimal Periodic Solutions of First-order Hamiltonian Systems with Anisotropic Growth, Discr. Cont. dyn. Sys. 37(3)(2017), 1559-1574. (with Zhang X.)

28. A note on the relations between the various index theories. J. Fixed Point Theory Appl. 19 (2017), no. 1, 617–648.

29. Subharmonic Pl-solutions of first order Hamiltonian systems. J. Math. Anal. Appl. 453 (2017), no. 1, 338–359. (with Tang S.).

30. Minimal P-symmetric period problem of first-order autonomous Hamiltonian systems. Front. Math. China 12 (2017), no. 3, 641–654. (with Zhou B.).

31. Infinitely many non-radial solutions for fractional Nirenberg problem. Calc. Var. Partial Differential Equations 56 (2017), no. 2, Paper No. 52, 40 pp. (with Ren Q.).

32. Relative index theories and applications. Topol. Methods Nonlinear Anal. 49(2)(2017), 587-614.

33. Q. Zhang & C. Liu, Homoclinic orbits for a class of first order nonperiodic Hamiltonian systems. Nonlinear Anal. Real World Appl. 41 (2018), 34–52. (with Zhang Q.).

34. Existence results for the fractional Q-curvature problem on three dimensional CR sphere. Commun. Pure Appl. Anal. 17 (2018), no. 3, 849–885. (with Wang Y.).

35. Multi-bump solutions for fractional Nirenberg problem. Nonlinear Anal. 171 (2018), 177–207. (with Ren Q.).

36. Uniqueness of types of infinitely-many-bump solutions for the fractional Nirenberg problem. J. Math. Anal. Appl. 468 (2018), no. 1, 1–37. (with Ren Q.).

37. Zhang, Xiaofei; Minimal periodic solutions of first-order convex Hamiltonian systems with anisotropic growth. Front. Math. China 13 (2018), no. 5, 1063–1073. (with Zuo. L.).

38. Stability of subharmonic solutions of first order Hamiltonian systems with anisotropic growth. Acta Math. Scientia, 39B(1) (2019), 111-118. (with Zhang X.).

39. Positive solutions of Yamabe-type equations with function coefficients on graphs. J. Math. Anal. Appl. 473 (2019), no. 2, 1343–1357. (with Zuo. L.).

40. Brake orbits of first order convex Hamiltonian systems with particular anisotropic growth. Acta Mathematica Sinica, English Series, 36(2)(2020), 171-178. (with Zhang X.).

41. The existence of ground state solution to elliptic equation with exponential growth on complete noncompact Riemannian manifold. J. Inequal. Appl. 2020, 1–21. (with Liu Y.).

42. Ground state solution and multiple solutions to elliptic equations with exponential growth and singular term. Comm. Pure and Appl. Anal. 19(5)(2020), 2819-2838. (with Liu Y.).

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