数学物理学报(英文版) ›› 1991, Vol. 11 ›› Issue (4): 433-441.

• 论文 • 上一篇    下一篇

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND-ORDER RETARDED DIFFERENTIAL EQUATIONS

王明新1,2, 张秦2   

  1. 1. Dept. of Math., Henan University, Zhengzhou, China;
    2. Dept. of Appl. Math., Beijing Inst. of Tech., Beijing, China
  • 收稿日期:1988-09-20 修回日期:1990-10-12 出版日期:1991-12-25 发布日期:1991-12-25

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND-ORDER RETARDED DIFFERENTIAL EQUATIONS

Wang Mingxin1,2, Zhang Qin2   

  1. 1. Dept. of Math., Henan University, Zhengzhou, China;
    2. Dept. of Appl. Math., Beijing Inst. of Tech., Beijing, China
  • Received:1988-09-20 Revised:1990-10-12 Online:1991-12-25 Published:1991-12-25

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摘要： In this paper, we consider the following second order retarded differential equations
x″(t)+cx'(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, l, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).

Abstract: In this paper, we consider the following second order retarded differential equations
x″(t)+cx'(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, l, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).

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