| 带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则 |
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| 引用本文： | 寇静,仉志余.带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则[J].高校应用数学学报(A辑),2021,36(1):70-82. |
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| 作者姓名： | 寇静 仉志余 |
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| 作者单位： | 太原工业学院理学系,山西太原030008;太原工业学院理学系,山西太原030008 |
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| 基金项目： | 国家自然科学基金(11701528,11647034);山西省自然科学基金(2011011002-3)。 |
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| 摘 要： | 研究一类带次线性中立项的二阶非线性广义Emden-Fowler时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程多个简便的Philos型和Kamenev型新振动准则.所得定理也适应于包括经典Euler方程等线性非中立型方程,推广和改进了已有文献中的相应结果.最后还给出应用实例展示了所得定理是有效和便捷的.
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| 关 键 词： | Emden-Fowler方程 Euler方程 二阶时滞微分方程 次线性中立项 振动准则 |
Philos-type oscillation criteria of second-order generalized Emden-Fowler delay differential equations with a sub-linear neutral term |
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| KOU Jing,ZHANG Zhi-yu.Philos-type oscillation criteria of second-order generalized Emden-Fowler delay differential equations with a sub-linear neutral term[J].Applied Mathematics A Journal of Chinese Universities,2021,36(1):70-82. |
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| Authors: | KOU Jing ZHANG Zhi-yu |
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| Institution: | (Department of Science,Taiyuan Institute of Technology,Shanxi 030008,China) |
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| Abstract: | In this paper,the oscillation of second order generalized Emden-Fowler delay differential equations with a sub-linear neutral term are studied.Under the non-canonical condition,by using Riccati transformation and the inequalities technique,several simple new Philos-type and Kamenev-type criteria of this kind of equations to ensure that every solution oscillates are established.These oscillation criteria generalize and improve the classic research results including those adapted to Euler equations established in previous literature.Finally,two application examples is given to show that these oscillation criteria obtained in this paper are effective and convenient. |
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| Keywords: | Emden-Fowler equation Euler equation second-order delay differential equation sub-linear neutral term oscillation criterion |
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