广义中立型Emden-Fowler方程的振动准则

数学物理学报 ›› 2016, Vol. 36 ›› Issue (6): 1067-1081.

广义中立型Emden-Fowler方程的振动准则

曾云辉¹, 罗李平¹, 俞元洪²

1. 衡阳师范学院数学与统计学院湖南衡阳 421002;
2. 中国科学院数学与系统科学研究院北京 100190

收稿日期:2016-07-07 修回日期:2016-11-08 出版日期:2016-12-26 发布日期:2016-12-26
作者简介:曾云辉,chj8121912@sina.com
基金资助:
湖南省“十三五”重点建设学科项目（[2016]）和湖南省教育厅科研基金（14C0170）资助

Oscillation Criteria for Generalized Neutral Emden-Fowler Equations

Zeng Yunhui¹, Luo Liping¹, Yu Yuanhong²

1. College of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421002;
2. Academy of System Sciences, Chinese Academy of Sciences, Beijing 100190

Received:2016-07-07 Revised:2016-11-08 Online:2016-12-26 Published:2016-12-26
Supported by:
Supported by the Construct Program of the Key Discipline in Hunan Province ([2016]) and the Natural Science Foundation of Education Department of Hunan Province (14C0170)

摘要/Abstract

摘要：

该文建立了广义中立型Emden-Fowler方程
（r（t）|y'（t）|^α-1y'（t））'+f（t，x （σ（t）））=0，t≥t₀
的若干新的振动准则，其中α>0，y（t）=x（t）+p（t）x（τ（t）），-μ≤p（t）≤1，μ∈（0，1）.所得的结果改进和推广了最近文献中的一些结果.也给出了说明所得结果的重要性的例子.

关键词: Emden-Fowler方程, 半线性微分方程, Riccati方法, 振动准则

Abstract:

Oscillation criteria are established for generalized neutral Emden-Fowler equations of the form
(r(t)|y'(t)|^α-1y'(t))'+f(t,x(σ(t)))=0, t≥t₀,
where α>0,y(t)=x(t)+p(t)x(τ(t)),-μ≤p(t)≤1,μ∈(0,1). Our results improve and extend some known results in the literature, recently. Some illustrating examples are also provided to show the importance of our results.

Key words: Emden-Fowler equation, Half-linear differential equation, Riccati method, Oscillation criterion

中图分类号:

O175.27

曾云辉, 罗李平, 俞元洪. 广义中立型Emden-Fowler方程的振动准则[J]. 数学物理学报, 2016, 36(6): 1067-1081.

Zeng Yunhui, Luo Liping, Yu Yuanhong. Oscillation Criteria for Generalized Neutral Emden-Fowler Equations[J]. Acta mathematica scientia,Series A, 2016, 36(6): 1067-1081.

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