• 论文 •

### 具有分布时滞的二阶非线性中立型时标动力方程的振动定理

1. (1)湖南工程学院理学院, 湖南 411104;(2)湖南工程学院成人教育学院, 湖南 411104
• 收稿日期:2008-07-03 修回日期:2009-02-04 出版日期:2010-09-25 发布日期:2010-09-25

CHEN Daxue;LIU Jiechun. Oscillation Theorems for Second-Order Nonlinear Neutral Dynamic Equations on Time Scales with Distributed Delay[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(9): 1191-1205.

### Oscillation Theorems for Second-Order Nonlinear Neutral Dynamic Equations on Time Scales with Distributed Delay

CHEN Daxue(1), LIU Jiechun(2)

1. (1)College of Science, Hunan Institute of Engineering, Hunan 411104;(2)Adult Education College, Hunan Institute of Engineering, Hunan 411104
• Received:2008-07-03 Revised:2009-02-04 Online:2010-09-25 Published:2010-09-25

$\big(r(t)\big(\big(y(t)+p(t)y(\tau(t))\big)^{\it \Delta}\big)^\beta\big)^{\it \Delta}+\int_c^dF(t,\xi,y(\delta(t,\xi))){\it \Delta}\xi=0$

This paper is concerned with the oscillation of the second-order nonlinear neutral dynamic equation with distributed delay
$\big(r(t)\big(\big(y(t)+p(t)y(\tau(t))\big)^{\it \Delta}\big)^\beta\big)^{\it \Delta}+\int_c^dF(t,\xi,y(\delta(t,\xi))){\it \Delta}\xi=0,$
on an arbitrary time scale $\mathbb{T}$, where $\beta>0$ is a quotient of odd positive integers. By employing the generalized Riccati transformation technique,
several sufficient conditions for all solutions of the equation be oscillatory. The results extend and improve some known results. Some examples to illustrate the main results are given.

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