Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2016, Vol. 52 ›› Issue (4): 588-591.DOI: 10.13209/j.0479-8023.2016.078

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Two Kinds of Gradient Representations for Nielsen Equations

MEI Fengxiang1, WU Huibin2, LI Yanmin3   

  1. 1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081
    2. School of Mathematics, Beijing Institute of technology, Beijing 100081 
    3. Department of Physics and Information Engineering, Shangqiu Normal College, Shangqiu 476000
  • Received:2015-10-07 Revised:2016-02-07 Online:2016-07-20 Published:2016-07-20
  • Contact: MEI Fengxiang,E-mail: meifx(at)


梅凤翔1, 吴惠彬2 , 李彦敏3   

  1. 1. 北京理工大学宇航学院, 北京 100081 
    2. 北京理工大学数学学院, 北京 100081
    3. 商丘师范学院物理与电气信息学院, 商丘 476000
  • 通讯作者: 梅凤翔,E-mail: meifx(at)
  • 基金资助:
    国家自然科学基金(10932002,11272050, 11372169)资助


The two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which the Nielsen equations can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of solution of the Nielsen equations. Some examples are given to illustrate the application of the results.

Key words: Nielsen equation, generalized gradient system, stability


提出两类广义梯度系统, 并研究其性质。给出 Nielsen 方程成为广义梯度系统的条件。利用广义梯度系统的性质, 研究Nielsen 方程解的稳定性。举例说明结果的应用。

关键词: Nielsen 方程, 广义梯度系统, 稳定性

CLC Number: