| 摘要: |
| 利用Riccati技巧以及积分平均技巧,得到判别二阶微分方程(r(t)ψ(x(t))x'(t))'+p(t)f(x(t))g(x('t))=0,二阶非线性时滞微分方程(r(t)ψ(x(t))x'(t))'+p(t)f(x(τ(t)))g(x('t))=0和(r(t)ψ(x(t))x'(t))'+p(t)f(x(t),x(τ(t)))g(x('t))=0,其中t ≥ t0,振动的3个新的充分性定理.利用这3个新的充分性定理可以简单地判断方程的振动性. |
| 关键词: 微分方程 振动 Riccati变换 |
| DOI： |
| 投稿时间：2005-06-29修订日期：2005-08-29 |
| 基金项目: |
|
| Oscillation of a Class of Second Order Nonlinear Differential Equation |
|
JIA Dui-hong, TANG Qing-gan
|
| (Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China) |
| Abstract: |
| In this paper,we discuss a class of the second order nonlinear different equation:(r(t)ψ(x(t))x'(t))'+p(t)f(x(t))g(x('t))=0,t ≥ t0,and the second order nonlinear delay different equation:(r(t)ψ(x(t))x'(t))'+p(t)f(x(τ(t)))g(x'(t))=0,(r(t)ψ(x(t))x'(t))'+p(t)f(x(t),x(τ(t)))g(x'(t))=0,t ≥ t0.We obtain three new sufficient condition by the Riccati-type transformation and integral technique.By these oscillation theorems,we can simply estimate the oscillation of the equation. |
| Key words: differential equation oscillation Riccati-type transformation |
