时间尺度上三阶Emden-Fowler动力方程的振动准则

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 222-232.

时间尺度上三阶Emden-Fowler动力方程的振动准则

李同兴^1,2, 韩振来^1,2, 张承慧², 孙一冰¹

1.济南大学数学科学学院济南 250022|2.山东大学控制科学与工程学院济南 250061

收稿日期:2010-09-30 修回日期:2011-08-15 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家自然科学基金(11071143, 60904024, 11026112)、山东省自然科学基金(ZR2010AL002, ZR2009AL003, Y2008A28)、山东省高等学校科技计划项目(J11LA01)和济南大学博士基金(XBS0843)资助

Oscillation Criteria for Third-order Emden-Fowler Delay Dynamic Equations on Time Scales

LI Tong-Xin^1,2, HAN Zhen-Lai^1,2, ZHANG Cheng-Hui², SUN Yi-Bing¹

1 School of Mathematics, University of Jinan, Jinan 250022;
2.School of Control Science and Engineering, Shandong University, Jinan 250061

Received:2010-09-30 Revised:2011-08-15 Online:2012-02-25 Published:2012-02-25
Supported by:
国家自然科学基金(11071143, 60904024, 11026112)、山东省自然科学基金(ZR2010AL002, ZR2009AL003, Y2008A28)、山东省高等学校科技计划项目(J11LA01)和济南大学博士基金(XBS0843)资助

摘要/Abstract

摘要：

运用Riccati 变换技术, 研究了时间尺度T上三阶Emden-Fowler时滞动力方程

(a(t)(r(t)x^? (t))^? ) ^?+p(t)x^γ (τ(t)) = 0
的振动性, 这里γ>0是正奇数的比, a, r, p是定义在T上的正的实值rd -连续函数. 得到一些新的振动结果, 推广和丰富了已有文献中的结论. 另外, 还给出了几个例子说明主要结果的合理性.

关键词: 振动性, 三阶, 时滞动力方程, 时间尺度

Abstract:

By means of Riccati transformation technique, the authors establish some new oscillation criteria for the third-order Emden-Fowler delay dynamic equations
(a(t)(r(t)x^? (t))^? ) ^?+p(t)x^γ (τ(t)) = 0
on a time scales , where γ > 0 is a quotient of odd positive integers, a, r, p are real-valued T positive rd-continuous functions defined on . Some new oscillation results which deal with T some cases not covered by existing results in the literature are obtained. Some examples are considered to illustrate the main results.

Key words: Third-order, Delay dynamic equations, Time scales

中图分类号:

39A21

李同兴, 韩振来, 张承慧, 孙一冰. 时间尺度上三阶Emden-Fowler动力方程的振动准则[J]. 数学物理学报, 2012, 32(1): 222-232.

LI Tong-Xin, HAN Zhen-Lai, ZHANG Cheng-Hui, SUN Yi-Bing. Oscillation Criteria for Third-order Emden-Fowler Delay Dynamic Equations on Time Scales[J]. Acta mathematica scientia,Series A, 2012, 32(1): 222-232.

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