Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (7): 842-845.

• 论文 • 上一篇    下一篇

QUALITATIVE ANALYSIS FOR A CLASS OF SECOND-ORDER NONLINEAR SYSTEM WITH DELAY

彭奇林   

  1. Department of Basic Science, Suqian Vocational and Technological College, Suqian, Jiangsu 223800
  • 收稿日期:1999-12-27 修回日期:2001-01-08 出版日期:2001-07-18 发布日期:2001-07-18

QUALITATIVE ANALYSIS FOR A CLASS OF SECOND-ORDER NONLINEAR SYSTEM WITH DELAY

PENG Qi-lin   

  1. Department of Basic Science, Suqian Vocational and Technological College, Suqian, Jiangsu 223800
  • Received:1999-12-27 Revised:2001-01-08 Online:2001-07-18 Published:2001-07-18

摘要: The second-order nonlinear system with delay x"(t)+f(x(t),x'(t))+g(x(t),x'(t))ψ(x(t-τ))=p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscillation are obtained by means of the Liapunov’s second method. The conclusion in the literatures are generalized.

Abstract: The second-order nonlinear system with delay x"(t)+f(x(t),x'(t))+g(x(t),x'(t))ψ(x(t-τ))=p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscillation are obtained by means of the Liapunov’s second method. The conclusion in the literatures are generalized.

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