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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (3): 302-308    DOI: 10.3785/j.issn.1008-9497.2019.03.006
数学与计算机科学     
一类二阶Emden-Fowler型微分方程的若干振动条件
杨甲山1,2, 覃桂茳1,2, 覃学文1,2, 赵春茹1,2
1.梧州学院 大数据与软件工程学院, 广西 梧州 543002
2.梧州学院 广西高校行业软件技术重点实验室,广西 梧州 543002
New oscillatory conditions of a class of the second-order Emden-Fowler differential equations
Jiashan YANG1,2, Guijiang QIN1,2, Xuewen QIN1,2, Chunru ZHAO1,2
1.School of Data Science and Software Engineering, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China
2.Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China
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摘要： 利用Riccati变换技术，借助Bernoulli不等式和Yang不等式以及数学分析技巧，研究了具有非线性中立项的二阶广义Emden-Fowler型微分方程的振动性，考虑非正则情形∫t0+∞a-1/β(t)dt<+∞，建立了该方程的若干振动准则。最后用2个例子说明，这些准则推广并改进了一些已有的结果，且具有较好的实用性和可操作性。
关键词： 振动性;  Emden-Fowler型微分方程;  非线性中立项;  Riccati变换    
Abstract: We investigate the oscillatory behavior of a class of the second-order generalized Emden-Fowler-type differential equations with a nonlinear neutral term the concerned equation is in a noncanonical form, i.e.∫t0+∞a-1/β(t)dt<+∞. By using the generalized Riccati transformation, Bernoulli inequality, Yang inequality and integral averaging technique, we establish some new oscillation criterions for the equations. Two illustrative examples are provided to show that our results extend and improve those reported in the literature, and have practicability and maneuverability.
Key words: oscillation    Emden-Fowle differential equation    nonlinear neutral    Riccati transformation
收稿日期: 2017-10-16 出版日期: 2019-05-25
CLC:  O175. 7  
基金资助: 国家自然科学基金资助项目(51765060)；梧州学院2016年校级科研重点项目(2016B008)；广西教育厅科研基金项目（2018KY0543）.
通讯作者: ORCID：http://orcid.org/0000-0002-5064-9225， E-mail: 57841824@qq.com.     E-mail: 57841824@qq.com.
作者简介: 杨甲山（1963—），ORCID：http://orcid.org/0000-0002-0340-097X，男，教授，主要从事微分方程的理论与应用研究，E-mail:syxyyjs@163.com.
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引用本文:

杨甲山, 覃桂茳, 覃学文, 赵春茹. 一类二阶Emden-Fowler型微分方程的若干振动条件[J]. 浙江大学学报（理学版）, 2019, 46(3): 302-308.

Jiashan YANG, Guijiang QIN, Xuewen QIN, Chunru ZHAO. New oscillatory conditions of a class of the second-order Emden-Fowler differential equations. Journal of ZheJIang University(Science Edition), 2019, 46(3): 302-308.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.03.006    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I3/302

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