刘春根
教授 博士生导师
所属大学: 广州大学
所属学院: 数学与信息科学学院
个人简介
个人基本信息
刘春根,男,1962年出生,湖南省耒阳市人
1978年-1981年,在湖南郴州师专(现湘南学院)数学系学习
1981年-1989年,在耒阳二中任教。期间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。
1992年-2017年,在南开大学数学学院任教。期间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
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。
各种奖项:
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年享受国务院政府津贴
研究基金:
国家自然科学基金:“整体分析与微分几何中的若干问题”,批准号:10071040,起止年限:2001.1-2003.12
全国优秀博士论文基金:“哈密顿系统与微分几何中的若干问题研究”,批准号:200014,起止年限:2001.1-2005.12
教育部留学回国人员启动基金:“辛几何与辛拓扑中一些问题的研究”,批准号:教外司留(2003)406号,起止年限:2003.1-2005.12
国家自然科学基金重点项目:“Hamilton系统及辛几何”,批准号:10531050,起止年限:2006.1-2009.12
国家重大基础研究发展计划(973):“动力系统大范围演化理论及其应用”,批准号:2006CB805903,起止年限:2006.1-2010.12
国家自然科学基金创新群体:“微分几何”,批准号:10621101,起止年限:2007.1-2015.12
国家自然科学基金:“非线性分析与辛几何中的若干问题的研究”,批准号:11071127,起止年限:2011.1-2013.12
国家重大基础研究发展计划(973):“无穷维系统的分析与控制”,批准号:2011CB808002,起止年限:2011.1-2015.12
教育部博士点基金:“哈密顿系统与辛几何中一些问题的研究”,批准号:20110031110003,起止年限:2011.1-2014.12
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
研究领域
Hamilton动力系统。
辛几何与辛拓扑。
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。
近期论文
1.C.Liu&S.TangSubharmonicPl-solutionsoffirstorderHamiltoniansystems.J.Math.Anal.Appl.453(2017),no.1,338–359.
2.C.Liu&X.ZhangSubharmonicsolutionsandminimalperiodicsolutionsoffirst-orderHamiltoniansystemswithanisotropicgrowth.DiscreteContin.Dyn.Syst.37(2017),no.3,1559–1574.
3.C.Liu&B.ZhouMinimalP-symmetricperiodproblemoffirst-orderautonomousHamiltoniansystems.Front.Math.China12(2017),no.3,641–654.
4.C.Liu&Q.RenInfinitelymanynon-radialsolutionsforfractionalNirenbergproblem.Calc.Var.PartialDifferentialEquations56(2017),no.2,PaperNo.52,40pp.
5.C.Liu,Anoteontherelationsbetweenthevariousindextheories.J.FixedPointTheoryAppl.19(2017),no.1,617–648.
6.Y.Chen,C.Liu,Groundstatesolutionsfornon-autonomousfractionalChoquardequations,Nonlinearity29(2016)1827–1842.
7.Y.Chen,C.Liu&Y.Zheng,ExistenceresultsforthefractionalNirenbergproblem,JournalofFunctionalAnalysis,270(2016)4043–4086.
8.Wang,Qi;Liu,Chungen;Anewindextheoryforlinearself-adjointoperatorequationsanditsapplications.J.DifferentialEquations260(2016)3749–3784.
9.C.Liu,S.Tang,Maslov(P;\omega)-IndexTheoryforSymplecticPaths.AdvancedNonlinearStudies15(2015),963–990.
10.C.Liu,,S.Tang,IterationinequalitiesoftheMaslovP-indextheorywithapplications.NonlinearAnal.127(2015),215–234.
11.C.Liu,Y.Zheng,OnsolitonsolutionsforaclassofdiscreteSchrodingersystems,Advancesindifferentialequationsandcontrolprocesses,15(1),2015,19-43.
12.C.Liu,OntheLagrangianboundaryproblemofHamiltoniansystemsandSeifertconjecture,AdvancesinMathematics(China).44(2)(2015),161-169.
13.LiuChungen&RenQiang,Onthesteady-statesolutionsofanonlinearphotoniclatticemodel,JournalofMathematicalPhysics56,031501(2015);doi:10.1063/1.4914333
14.Wang,Qi;Liu,Chungen;TherelativeMorseindextheoryforinfinitedimensionalHamiltoniansystemswithapplications.J.Math.Anal.Appl.427(2015),no.1,17–30.
15.LiuC.ZhangD.Seifertconjectureintheevenconvexcase.toappearinComm.PureAppl.Math.67(2014),no.10,1563–1604.
16.D.ZhangandC.Liu,Multiplebrakeorbitsoncompactconvexsymmetricreversiblehypersurfacesin$\R^{2n}$.Annalesdel'InstitutHenriPoincaré:AnalyseNonLinéaire.31(2014),no.3,531–554.
17.D.ZhangandC.Liu,Multiplicityofbrakeorbitsoncompactconvexsymmetricreversiblehypersurfacesin$\R^{2n}$for$n\ge4$,ProceedingsofLondonMathematicalSociety.107(2013),no.3,1-38.
18.Liu.CandZheng.Y.OnsolitonsolutionsofaclassofSchrodinger-KdVsystem,ProceedingsoftheAmericanMathematicalSociety.141(2013),no.10,3477–3484
19.Q.ZhangandC.Liu,Multiplesolutionsforaclassofsemilinearellipticequationswithgeneralpotentials,NonlinearAnalysis,75(no.14)(2012)5473–5481.
20.LiuCandZhangQ.,NontrivialsolutionsforasmptoticallylinearHamiltoniansystemswithLagrangianboundaryconditions.ActaMatematicaScientia,2012,32B(4):1545-1558.
21.C.Liu,PeriodicsolutionsofasymptoticallylineardelaydifferentialsystemsviaHamiltoniansystems,J.DifferentialEquations,252(no.10)(2012)5712–5734.
22.C.Liu,Q.Wang,SymmetricalSymplecticCapacitywithApplications,DISCRETEANDCONTINUOUSDYNAMICALSYSTEMS,Volume32,Number6,June2012,pp.2253-2270.
23.LiuC,ZhangD.Brakeorbitsinboundedconvexsymmetricdomains.Progressinvariationalmethods,71–89,NankaiSer.PureAppl.Math.Theoret.Phys.,7,WorldSci.Publ.,Hackensack,NJ,2011.
24.ZhangQ.andLiuC.InfinitelymanyperiodicsolutionsforsecondorderHamiltoniansystems.JournalofDifferentialEquations,251(no.4-5)(2011),816-833.
25.Liu.CandZheng.Y.Existenceofnontrivialsolutionsforp-LaplacianequationsinR^NJournalofMathematicalAnalysisandApplicationsVol.380(2),2011,669-679.
26.Liu.CandZheng.Y.LinkingSolutionsfor$p$-LaplaceEquationswithNonlinearBoundaryConditionsandIndefiniteWeight,Calc.Var.PartialDifferentialEquations41(no.1-2)(2011),261-284.
27.LiuC.andZhangQ.ExistenceandMultiplicityofHomoclinicSolutionsfortheSecondOrderHamiltoniansystems,InternationalMathematicalForum,Vol.6,2011,no.4,159–176.
28.LiuC.andWangQ.Someabstractcriticalpointtheoremforself-adjointoperatorequations.Chin.Ann.Math.32B(1),2011,1-14.
29.Tian,Y.Liu,C.Multiplepositivesolutionstoanonhomogeneousboundaryvalueproblemforaclassofthird-orderp-Laplacianequations.(Chinese)Adv.Math.(China)40(1)(2011),71–78.
30.LiuC.,WangQ.andLinX.,AnindextheoryforsymplecticpathsassociatedwithtwoLagrangiansubspaceswithapplications.Nonlinearity.24(1)(2011),43-70.
31.LiChong&LIUChunGen,BrakesubharmonicsolutionsoffirstorderHamiltoniansystems,SCIENCECHINA(Mathematics),2010,Vol.53.No.10:2719–2732
32.Y.TianandC.Liu,MultiplicityofpositivesolutionstoM-pointboundaryvalueproblemofsecondorderimpulsivedifferentialequations,ActaMath.Appl.Sinica(EnglishSeries),26(1)(2010),145-158.
33.QingyeZhang,ChungenLiu,InfinitelymanyhomoclinicsolutionsforsecondorderHamiltoniansystems,NonlinearAnalysis,72(2)(2010),894-903
34.C.Liu,MinimalperiodestimatesforbrakeorbitsofnonlinearsymmetricHamiltoniansystems,Discreteandcontinuousdynamicalsystems,27(1)(2010),337-355.
35.C.LIandC.Liu,TheexistenceofnontrivialsolutionsofHamiltoniansystemswithLagrangianboundaryconditions,ActaMathematicaScientia,2009,29B(2),313-326.
36.GuoF.andLiuC,MultiplicityofcharacteristicswithLagrangianboundaryvaluesonsymmetricstar-shapedhypersurfaces.J.Math.Anal.Appl.353(1)(2009),88-98.
37.GuoF.andLiuC.MultiplicityofLagrangianorbitsonsymmetricstar-shapedhypersurfaces.NonlinearAnal.69(2008),no.4,1425--1436.
38.C.LIandC.Liu,NontrivialsolutionsofsuperquadraticHamiltoniansystemswithLagrangianboundaryconditionsandtheL-indextheory.ChineseAnn.Math.29(6)2008,597-610.
39.Chun-genLiu,Maslov-typeindextheoryforsymplecticpathswithLagrangianboundaryconditions,AdvancedNonlinearStudies,7(1)(2007),131-161.
40.Chun-genLiu,AsymptoticallylinearHamiltoniansystemswithLagrangianboundaryconditions.PacificJ.Math.232(2007),no.1,233--255.
41.LiuChungen,TheMorsetheoryandthemaslov-typeindextheory,BulletinoftheInstituteofMathematics,AcademiaSinica(NewSeries),Vol.1(2006),No.3,pp.341-395.
42.LiuChungen,Maslov$P$-indextheoryforasymplecticpathwithapplications,ChineseAnn.Math.27B(4),441-458,2006.
43.LiuChungen,AnoteonthemonotonicityofMaslov-typeindexoflinearHamiltoniansystemswithapplications,ProceedingsoftheRoyalSocietyofEdinburgh,135A(no.6),1263-1277,2005.
44.Chun-genLiu,TherelationoftheMorseindexofclosedgeodesicswiththeMaslov-typeindexofsymplecticpaths,ActaMathematicaSinica,EnglishSeries,21(2),2005,237-248.
45.Chun-GenLiu,Cup-lengthestimateforLagrangianintersections.JournalofDifferentialEquations209(1)(2005)57-76.
46.Chun-genLiu,YimingLongandChaofengZhu,Multiplicityofclosedcharacteristicsonsymmetricconvexhypersurfacesin$\R^{2n}$.Math.Ann,323(no.2)(2002)201-215。
47.Chun-genLiu&YimingLong,Iteratedindexformulaeforclosedgeodesicswithapplications,ScienceinChina(2002)vol.45No.1(9-28)
48.C.LiuandY.Long,IterationinequalitiesofMaslov-typeindextheorywithapplications.JournalofDifferentialEquations.165(no.2)(2000)355-376.
49.C.Liu,ThestabilityoftheperiodicsolutionsofsecondorderHamiltoniansystems.Chin.Ann.ofMath.21B:2(2000),225-232.
50.C.Liu,SubharmonicsolutionsofHamiltoniansystems,Nonlinearanalysis,42(2)(2000),185-198
51.C.LiuandY.Long,Hyperboliccharacteristicsonstar-shapedhypersurfaces,Ann.I.H.P.Ana.Nonlinéaire.16(6),(1999)725-746.
52.C.Liu,ThestabilityofsubharmonicsolutionsforHamiltoniansystems.JournalofMathematicalAnalysisandApplications.240(2)(1999),491-504.
53.C.LiuandY.Long,AnOptimalestimateofMaslov-typeindex,ChineseSci.Bull,vol.43(no.13)(1998),pp1063-1066.
54.C.Liu,Relativeindextheoriesandapplications.Topol.MethodsNonlinearAnal.49(2)(2017),587-614.
55.Q.Zhang&C.Liu,HomoclinicorbitsforaclassoffirstordernonperiodicHamiltoniansystems.NonlinearAnal.RealWorldAppl.41(2018),34–52.