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欧阳自根教授
2019-01-11 17:40     (点击:)


    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James S.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.

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)。

发表论文:

[1]Xiao, Qizhen; Liu, Hongliang; Ouyang, Zigen,Existence and concentration of a nonlinear biharmonic equation with sign-changing potentials and indefinite nonlinearity,ADVANCES IN DIFFERENCE EQUATIONS,Article Number: 384 Published: OCT 23 2018(SCI).

[2]Zhou, Chengfang; Ouyang, Zigen,Existence of nontrivial solutions for a class of biharmonic equations with singular potential in R-N,BOUNDARY VALUE PROBLEMS Article Number: 19 Published: FEB 8 2018(SCI).

[3]Liu, Zhisu; Ouyang, Zigen,Existence of positive ground state solutions for fractional Schrodinger equations with a general nonlinearity,APPLICABLE ANALYSIS, 97(7)(2018),1154-1171(SCI).

[4]Chen, Huiwen; He, Zhimin; Li, Jianli,Ouyang,Zigen,New Results for Second Order Discrete Hamiltonian Systems,TAIWANESE JOURNAL OF MATHEMATICS, 21( 2)(2017), 403-428(SCI).

[5]Yang, Liu; Liu, Zhisu; Ouyang, Zigen,Multiplicity results for the Kirchhoff type equations with critical growth,APPLIED MATHEMATICS LETTERS,Volume: 63(2017),118-123(SCI).

[6]Chen, Huiwen; He, Zhimin; Ouyang, Zigen; et al.,Homoclinic orbits for damped vibration systems with asymptotically quadratic or subquadratic potentials,ADVANCES IN DIFFERENCE EQUATIONS,Article Number: 78,Published: MAR 16 2016(SCI).

[7] Huilan Wang, Zigen Ouyang* and Hengsheng Tang, A note on the shooting method and its applications in the Stieltjes integral boundary value problems, Boundary Value Problems (2015) 2015:102 DOI 10.1186/s13661-015-0359-8(SCI).

[8] Zigen Ouyang and Hongliang Liu, Solvability for a Fractional Order Three-Point Boundary Value System at Resonance, Abstract and Applied Analysis, Volume 2014, Article ID 419514, 15 pages(SCI).

[9] Dongyuan Liu and Zigen Ouyang, Solvability of Third-Order Three-Point Boundary

Value Problems, Abstract and Applied Analysis, Volume 2014, Article ID 793639, 7 pages(SCI).

[10] Zigen Ouyang and HuiWang, A Model for Influence of Nuclear-Electricity

Industry on Area Economy, Mathematical Problems in Engineering, Volume 2014, Article ID 792307, 7 pages(SCI).

[11] Hongliang Liu and Zigen Ouyang, Existence of solutions for second-order

three-point integral boundary value problems at resonance, Boundary Value Problems 2013, 2013:197, 1-11(SCI).

[12] Huilan Wang, Zigen Ouyang and Liguang Wang, Application of the shooting method to second-order multi-point integral boundary-value problems, Boundary Value Problems 2013, 2013:205, 1-10(SCI).

[13] Z.G. Ouyang,C.H. Ou, James S.R.Wong, Solvability of three-point boundary value problems with resonance,Communication in Applied Analysis,17(2013)47-60.

[14] Z. Ouyang, G. Li, Existence of the solutions for a class of nonlinear fractional order three-point boundary value problems with resonance, Boundary Value Problem, 2012,2012-68(SCI).

[15] Z.G. Ouyang,Chunhua Ou, Global Stability and convergence rate of traveling waves for a nonlocal model in periodic media, Discrete and Continuous Dynamical Systems, SERIES B,17(2012)(SCI).

[16] M.X. Liao, X.H. Tang, Zigen Ouyang, Changjin Xu,Dynamical properties of a class of higher-order nonlinear difference equations, Appl. Math. and Comput. , 217 (2011) 5476-5479(SCI) .

[17] Z.G. Ouyang, Y.M. Chen, S.L. Zou, Existence of positive solutions to a boundary value problem for a delayed nonlinear fractional differential system, Boundary Value Problem., Article ID 475126, 17pages, 2011(SCI).

[18] Z.G. Ouyang, Existence and uniqueness of the solutions for a class of nonlinear fractional partial differential equations with delay, Comp.& Math. with Appl., 61(2011)860-870(SCI).

[19] J.C. Zhong, Z.G. Ouyang, S.L. Zou,An oscillation theorem for a class of second-order forced neutral delay differential equations with mixed nonlinearities, Appl. Math. Lett.,24(2011) 1449-1454(SCI).

[20] Z.G. Ouyang, J.C. Zhong, S.L. Zou, Oscillation criteria for a class of second-order nonlinear differential equations with damping term,Abst. and Appl. Anal. Article ID 897058, 12 pages, 2009(SCI).

[21] F.Q. Yin, S.F. Zhou, Z.G. Ouyang, C.H. Xiao, Attractor for Lattice system of dissipative Zakaharov equation, Acta Mathematic Sinica: English Series, 61(2009)321-324(SCI).

[22] X.Y. Liao, Z.G. Ouyang and S.F. Zhou, Permanence of speciesin nonautonomous discrete Lotka-Volterra competitive system with delays and feedback controls, Journal of Comput. and Appl. Math., 211(1) (2008), 1-10(SCI).

[23]X.Y. Liao, Z.G. Ouyang and S.F. Zhou, Permanence and Stability of Equilibrium for a Two-Prey One-Predator Discrete Model, Appl. Mathe. and Comput., 186(2007), 93-100(SCI).

[24]Z.G.Ouyang S.L.Zou S.F.Zhou J.D.Liao,Invariant set and attracting set for a class of delay discrete parabolic systems,Int. J. Appl。 Math. and Appl,1(2008).

[20]X.Y. Liao, S.F. Zhou and Z.G. Ouyang, On a stoichiometric two predators on one prey discrete model, Appl. Mathe. Lett., 20 (2007), 272-278(SCI).

[25]Q. S. wang, Z. G. Ouyang, J. D. Liao, Oscillation and asymptotic behavior for a class of nonlinear delayed parabolic differential equations, Appl. Math. Lett. 32(2006)151-154 (SCI).

[26]J. H. Ma, S. F.Zhou, Z. G. Ouyang, Asymptotic synchronization in dissipative lattices of coupled oscillators, J. Math. Anal. Appl. Vol322, Issue 2(2006), 1111-1127 (SCI).

[27]S. F.Zhou, F. Q. Yin, Z. G. Ouyang, Random Attrator damped nonlinear wave equations with white noise, SIAM J. Applied Dynamical Systems, 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, Classifications and existence of positive

solutions of higher-order nonlinear neutral differential equations, Appl. Math. and Comput.,148(2004), 105-120(SCI).

[30]Z. G. Ouyang, S. F. Zhou, F. Q. Yin, Oscillation for a class of odd-order delay

paraboic differential equations, J. of Comp. and Appl. Math., 175(2005), 305-319(SCI).

[31]Z. G. Ouyang, S. F. Zhou, F. Q. yin, Oscillation for a class of neutral parabolic

differential equations, Comput. & Math. with Appl., 50(2005), 145-155(SCI).

[32]Z. G. Ouyang, Y. K. Li and M. C. Qing, Eventually solutions ofodd-oder neutral

differential equations, Appl. Math. Lett., 17(2004), 159-166(SCI).

[33]Z. G. Ouyang, Nnecessary and sufficientconditions for oscillation of odd order neutral delay parabolic differential equations, Appl. Math. Lett., 16(2003), 1039-1045(SCI).

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