数学季刊 ›› 2003, Vol. 18 ›› Issue (1): 7-12.

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李安纳特方程的稳定性和有界性

  

  1. Department of Mathematics,Anhui University,Hefei 230039,China
  • 收稿日期:2001-10-24 出版日期:2003-03-30 发布日期:2024-04-18
  • 作者简介:ZHOU Xian-feng(1968-),male ,native of Tianchang ,Auhui ,M.S.D.,engages in functional differential equation .
  • 基金资助:
    Supported by the National Natural Science Foundation of China(10241005)

Stability and Boundedness of Retarded Liénard-type Equation

  1. Department of Mathematics,Anhui University,Hefei 230039,China
  • Received:2001-10-24 Online:2003-03-30 Published:2024-04-18
  • About author:ZHOU Xian-feng(1968-),male ,native of Tianchang ,Auhui ,M.S.D.,engages in functional differential equation .
  • Supported by:
    Supported by the National Natural Science Foundation of China(10241005)

摘要: This paper aims to investigate the retarded Liénard-type equation
x+ f1( x)x˙ + f2( x)x˙( t  - τ) + f3( x)x˙2 + φ( x)+ g( x( t - τ)) = 0,
where τis a nonnegative constant ,f1 ,f2 ,f3 ,φ and g are continuous functions on R.Using Liapunov functional method ,we establish a sufficient condition on the stability and boundedness of the solutions of above equation.This will generalize the main results of reference[2].
Key words:retarded Liénard-type equation;stability ;boundedness
CLC number:O175.21    

关键词: retarded Liénard-type equation, stability , boundedness

Abstract: This paper aims to investigate the retarded Liénard-type equation
x+ f1( x)x˙ + f2( x)x˙( t  - τ) + f3( x)x˙2 + φ( x)+ g( x( t - τ)) = 0,
where τis a nonnegative constant ,f,f,f,φ and g are continuous functions on R.Using Liapunov functional method ,we establish a sufficient condition on the stability and boundedness of the solutions of above equation.This will generalize the main results of reference[2].
Key words:retarded Liénard-type equation;stability ;boundedness
CLC number:O175.21    

Key words: retarded Liénard-type equation, stability , boundedness

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