个人简介
欧阳自根，男，1965年生，理学博士，教授,硕士生导师.现任南华大学数理学院院长，湖南省中青年骨干教师，湖南省数学会常务理事，美国数学评论评论员。2010年4月-2011年4月由国家留学基金委公派赴纽芬兰纪念大学访问一年，在导师赵晓强、欧春华教授的指导下，在动力系统的行波解方面作了一些初步的研究。同时，通过与香港JamesS.R.Wong教授以及加拿大欧春华、陈玉明教授的合作，在微分方程边值问题领域尤其在具resonance的三边值问题领域作了卓有成效的工作。主要研究方向为微分方程及动力系统、核能经济与管理。自1989年以来一直在高校从事教学与科研工作.近年来主持完成省教委科研课题2项，省科技厅课题一项，省自然科学基金课题1项，作为主要成员，参与国家自然科学基金项目3项（第二）.有丰富的教学和科研能力，特别是在泛函微分方程、动力系统方面有较深入的研究经历.指导大学生参加全国数模竞赛获湖南赛区一、二等奖各一项，获美国大学生数模竞赛一等奖一项。近年来在国内外学术刊物上发表论文40余篇，其中在SCI源刊发表论文30余篇.
近期完成的主要课题：
1）具时滞的微分系统与格点系统的动力学行为研究，省教育厅青年基金（2005-2007），主持（已结题）；
2）格点系统与波动方程的时空行为，国家自然科学基金（2005-2007），第二（已结题）；
3）核电产业与区域经济的拟生态系统分析，湖南省科技厅（2009-2011），主持（已结题）；
4）核电产业与区域经济的动力系统分析，湖南省自然科学基金（2007-2008），第二（已结题）；
5）核电产业与区域经济的拟生态系统研究，国家博士后基金（2011.1-2012.12），主持（编号：66714，3.0万，已结题）。
6）具resonance的多点边值问题研究，湖南省自然科学基金（编号：13JJ3074，2013.1-2015.12），主持（3.0万，进展良好）。
7）具共振的边值问题，湖南省教育厅重点项目（编号13A088，2013.1-2015.12），主持（6.0万）。
近期论文
[1]Xiao,Qizhen;Liu,Hongliang;Ouyang,Zigen,Existenceandconcentrationofanonlinearbiharmonicequationwithsign-changingpotentialsandindefinitenonlinearity,ADVANCESINDIFFERENCEEQUATIONS,ArticleNumber:384Published:OCT232018(SCI).
[2]Zhou,Chengfang;Ouyang,Zigen,ExistenceofnontrivialsolutionsforaclassofbiharmonicequationswithsingularpotentialinR-N,BOUNDARYVALUEPROBLEMSArticleNumber:19Published:FEB82018(SCI).
[3]Liu,Zhisu;Ouyang,Zigen,ExistenceofpositivegroundstatesolutionsforfractionalSchrodingerequationswithageneralnonlinearity,APPLICABLEANALYSIS,97(7)(2018),1154-1171(SCI).
[4]Chen,Huiwen;He,Zhimin;Li,Jianli,Ouyang,Zigen,NewResultsforSecondOrderDiscreteHamiltonianSystems,TAIWANESEJOURNALOFMATHEMATICS,21(2)(2017),403-428(SCI).
[5]Yang,Liu;Liu,Zhisu;Ouyang,Zigen,MultiplicityresultsfortheKirchhofftypeequationswithcriticalgrowth,APPLIEDMATHEMATICSLETTERS,Volume:63(2017),118-123(SCI).
[6]Chen,Huiwen;He,Zhimin;Ouyang,Zigen;etal.，Homoclinicorbitsfordampedvibrationsystemswithasymptoticallyquadraticorsubquadraticpotentials，ADVANCESINDIFFERENCEEQUATIONS，ArticleNumber:78，Published:MAR162016(SCI).
[7]HuilanWang,ZigenOuyang*andHengshengTang,AnoteontheshootingmethodanditsapplicationsintheStieltjesintegralboundaryvalueproblems,BoundaryValueProblems(2015)2015:102DOI10.1186/s13661-015-0359-8(SCI).
[8]ZigenOuyangandHongliangLiu,SolvabilityforaFractionalOrderThree-PointBoundaryValueSystematResonance,AbstractandAppliedAnalysis,Volume2014,ArticleID419514,15pages(SCI).
[9]DongyuanLiuandZigenOuyang,SolvabilityofThird-OrderThree-PointBoundary
ValueProblems,AbstractandAppliedAnalysis,Volume2014,ArticleID793639,7pages(SCI).
[10]ZigenOuyangandHuiWang,AModelforInfluenceofNuclear-Electricity
IndustryonAreaEconomy,MathematicalProblemsinEngineering,Volume2014,ArticleID792307,7pages(SCI).
[11]HongliangLiuandZigenOuyang,Existenceofsolutionsforsecond-order
three-pointintegralboundaryvalueproblemsatresonance,BoundaryValueProblems2013,2013:197,1-11(SCI).
[12]HuilanWang,ZigenOuyangandLiguangWang,Applicationoftheshootingmethodtosecond-ordermulti-pointintegralboundary-valueproblems,BoundaryValueProblems2013,2013:205,1-10(SCI).
[13]Z.G.Ouyang，C.H.Ou,JamesS.R.Wong,Solvabilityofthree-pointboundaryvalueproblemswithresonance，CommunicationinAppliedAnalysis，17（2013）47-60.
[14]Z.Ouyang,G.Li,Existenceofthesolutionsforaclassofnonlinearfractionalorderthree-pointboundaryvalueproblemswithresonance,BoundaryValueProblem,2012,2012-68(SCI).
[15]Z.G.Ouyang，ChunhuaOu,GlobalStabilityandconvergencerateoftravelingwavesforanonlocalmodelinperiodicmedia,DiscreteandContinuousDynamicalSystems,SERIESB,17(2012)(SCI).
[16]M.X.Liao,X.H.Tang,ZigenOuyang,ChangjinXu,Dynamicalpropertiesofaclassofhigher-ordernonlineardifferenceequations,Appl.Math.andComput.,217(2011)5476-5479(SCI).
[17]Z.G.Ouyang,Y.M.Chen,S.L.Zou,Existenceofpositivesolutionstoaboundaryvalueproblemforadelayednonlinearfractionaldifferentialsystem,BoundaryValueProblem.,ArticleID475126,17pages,2011(SCI).
[18]Z.G.Ouyang,Existenceanduniquenessofthesolutionsforaclassofnonlinearfractionalpartialdifferentialequationswithdelay,Comp.&Math.withAppl.,61(2011)860-870(SCI).
[19]J.C.Zhong,Z.G.Ouyang,S.L.Zou,Anoscillationtheoremforaclassofsecond-orderforcedneutraldelaydifferentialequationswithmixednonlinearities,Appl.Math.Lett.,24(2011)1449-1454(SCI).
[20]Z.G.Ouyang,J.C.Zhong,S.L.Zou,Oscillationcriteriaforaclassofsecond-ordernonlineardifferentialequationswithdampingterm，Abst.andAppl.Anal.ArticleID897058,12pages,2009(SCI).
[21]F.Q.Yin,S.F.Zhou,Z.G.Ouyang,C.H.Xiao,AttractorforLatticesystemofdissipativeZakaharovequation,ActaMathematicSinica:EnglishSeries,61(2009)321-324(SCI).
[22]X.Y.Liao,Z.G.OuyangandS.F.Zhou,PermanenceofspeciesinnonautonomousdiscreteLotka-Volterracompetitivesystemwithdelaysandfeedbackcontrols,JournalofComput.andAppl.Math.,211(1)(2008),1-10(SCI).
[23]X.Y.Liao,Z.G.OuyangandS.F.Zhou,PermanenceandStabilityofEquilibriumforaTwo-PreyOne-PredatorDiscreteModel,Appl.Mathe.andComput.,186(2007),93-100(SCI).
[24]Z.G.OuyangS.L.ZouS.F.ZhouJ.D.Liao，Invariantsetandattractingsetforaclassofdelaydiscreteparabolicsystems，Int.J.Appl。Math.andAppl，1（2008）.
[20]X.Y.Liao,S.F.ZhouandZ.G.Ouyang,Onastoichiometrictwopredatorsononepreydiscretemodel,Appl.Mathe.Lett.,20(2007),272-278(SCI).
[25]Q.S.wang,Z.G.Ouyang,J.D.Liao,Oscillationandasymptoticbehaviorforaclassofnonlineardelayedparabolicdifferentialequations,Appl.Math.Lett.32(2006)151-154(SCI).
[26]J.H.Ma,S.F.Zhou,Z.G.Ouyang,Asymptoticsynchronizationindissipativelatticesofcoupledoscillators,J.Math.Anal.Appl.Vol322,Issue2（2006）,1111-1127(SCI).
[27]S.F.Zhou,F.Q.Yin,Z.G.Ouyang,RandomAttratordampednonlinearwaveequationswithwhitenoise,SIAMJ.AppliedDynamicalSystems，4(4)2005(SCI).
[28]欧阳自根,李永昆,偶数阶时滞微分方程的单调解,数学研究与评论,24(2004),321-327.
[29]Z.G.Ouyang,Y.K.Li,Q.G.Tang,Classificationsandexistenceofpositive
solutionsofhigher-ordernonlinearneutraldifferentialequations,Appl.Math.andComput.,148(2004),105-120(SCI).
[30]Z.G.Ouyang,S.F.Zhou,F.Q.Yin,Oscillationforaclassofodd-orderdelay
paraboicdifferentialequations,J.ofComp.andAppl.Math.,175(2005),305-319(SCI).
[31]Z.G.Ouyang,S.F.Zhou,F.Q.yin,Oscillationforaclassofneutralparabolic
differentialequations,Comput.&Math.withAppl.,50(2005),145-155(SCI).
[32]Z.G.Ouyang,Y.K.LiandM.C.Qing,Eventuallysolutionsofodd-oderneutral
differentialequations,Appl.Math.Lett.,17(2004),159-166(SCI).
[33]Z.G.Ouyang,Nnecessaryandsufficientconditionsforoscillationofoddorderneutraldelayparabolicdifferentialequations,Appl.Math.Lett.,16(2003),1039-1045(SCI).