具有次线性中立项的二阶Emden-Fowler时滞微分方程的振动性

曾云辉1,罗慧慧2,王益林1,罗李平1,俞元洪3

振动与冲击 ›› 2023, Vol. 42 ›› Issue (13) : 50-57.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (13) : 50-57.
论文

具有次线性中立项的二阶Emden-Fowler时滞微分方程的振动性

  • 曾云辉1,罗慧慧2,王益林1,罗李平1,俞元洪3
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Oscillation criteria of second order Emden-Fowler time-delay differential equations with a sub-linear neutral term

  • ZENG Yunhui1, LUO Huihui2, WANG Yilin1, LUO Liping1, YU Yuanhong3
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摘要

本文研究含有次线性中立项的二阶Emden-Fowler 时滞微分方程 解的振动性, 其中 均为正奇数之商, 利用Riccati变换,积分平均和不等式技巧,我们建立了方程的三个新的振动准则. 所得结果将经典的Leighton ]和Kneser 振动准则推广到含有次线性中立项的超线性Emden -Fowler时滞微分方程.而且,新的结果不仅推广和改进了最近文献中出现的关于该方程当 时的振动准则,同时也改进,推广和简化了方程当 或者 时的振动准则,所得准则的有效性通过若干例子给出了说明.

Abstract

The paper is devoted to the study of oscillation of solutions to second-order Emden-Fowler delay differential equations containing a sub-linear neutral term of the form  where  are quotient of odd positive integers, and  By using the Riccati substitution , integral averaging and inequality techniques, three new oscillation criteria for the equation are established. which extend classical Leighton and Kneser  oscillation criteria to super-linear Emden-Fowler delay differential equation. And, we not only extend but also improve several results about the cases of   or in the literature, recently. The effectiveness of the obtained criteria are illustrated via examples.

关键词

次线性中立项 / Emden-Fowler微分方程 / 振动准则

引用本文

导出引用
曾云辉1,罗慧慧2,王益林1,罗李平1,俞元洪3. 具有次线性中立项的二阶Emden-Fowler时滞微分方程的振动性[J]. 振动与冲击, 2023, 42(13): 50-57
ZENG Yunhui1, LUO Huihui2, WANG Yilin1, LUO Liping1, YU Yuanhong3. Oscillation criteria of second order Emden-Fowler time-delay differential equations with a sub-linear neutral term[J]. Journal of Vibration and Shock, 2023, 42(13): 50-57

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