| 一类二阶Emden-Fowler型微分方程的若干振动条件 |
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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), 1959, 46(3): 302-308. DOI: 10.3785/j.issn.1008-9497.2019.03.006 |
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| 作者姓名： | 杨甲山 覃桂茳 覃学文 赵春茹 |
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| 基金项目： | 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）. |
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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。
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| 关 键 词： | 振动性 Emden-Fowler型微分方程 非线性中立项 Riccati变换 |
| 收稿时间： | 2017-10-16 |
New oscillatory conditions of a class of the second-order Emden-Fowler differential equations |
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| Jiashan YANG,Guijiang QIN,Xuewen QIN,Chunru ZHAO. New oscillatory conditions of a class of the second-order Emden-Fowler differential equations[J]. Journal of Zhejiang University(Sciences Edition), 1959, 46(3): 302-308. DOI: 10.3785/j.issn.1008-9497.2019.03.006 |
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| Authors: | Jiashan YANG Guijiang QIN Xuewen QIN Chunru ZHAO |
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| Affiliation: | 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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| 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. |
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| Keywords: | oscillation Emden-Fowle differential equation nonlinear neutral Riccati transformation |
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