二阶广义Emden-Fowler型延迟微分方程的振荡性分析

数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1041-1054.

二阶广义Emden-Fowler型延迟微分方程的振荡性分析

李继猛()

邵阳学院理学院湖南邵阳 422004

收稿日期:2018-06-18 出版日期:2019-10-26 发布日期:2019-11-08
作者简介:李继猛, E-mail:syxyljm@163
基金资助:
湖南省自然科学基金(12JJ3008);湖南省教育厅教学改革研究项目(2016JG671);邵阳市科技计划项目(2016GX04)

Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations

Jimeng Li()

School of Science, Shaoyang University, Hunan Shaoyang 422004

Received:2018-06-18 Online:2019-10-26 Published:2019-11-08
Supported by:
the Hunan Natural Science Foundation(12JJ3008);the Research Project on Teaching Reform of Hunan Education Department(2016JG671);the Science and Technology Plan Project of Shaoyang City(2016GX04)

摘要/Abstract

摘要：

研究了一类二阶广义Emden-Fowler型非线性延迟泛函微分方程的振荡性.利用广义双Riccati变换技术及一些分析技巧，在正则和非正则两种情形下获得了该方程振荡的一系列新准则，推广且改进了现有文献中的一些结果，并给出了3个实例来说明文中的主要结论.

关键词: 振荡性, 延迟, Emden-Fowler型微分方程, Riccati变换

Abstract:

We study the oscillatory behavior of a class of second-order generalized EmdenFowler-type nonlinear delay functional differential equations in this paper. By using a couple generalized Riccati transformation and some necessary analytic techniques, we establish some new oscillation criteria for the equations under both the cases canonical form and noncanonical form, which deal with some cases not covered by existing results in the literature. Three examples are given to illustrate the main results of this article.

Key words: Oscillation, Delay, Emden-Fowler-type differential equation, Riccati transformation

中图分类号:

O175.27

李继猛. 二阶广义Emden-Fowler型延迟微分方程的振荡性分析[J]. 数学物理学报, 2019, 39(5): 1041-1054.

Jimeng Li. Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1041-1054.

参考文献

1	Dzurina J , Stavrouakis I P . Oscillation criteria for second order delay differential equations. Appl Math Comput, 2003, 14 (3): 445- 453
2	Sun Y G , Meng F W . Note on the paper of Dzurina and Stavroulakis. Appl Math Comput, 2006, 27 (4): 1634- 1641
3	黄记洲, 符策红. 广义Emden-Fowler方程的振动性. 应用数学学报, 2015, 38 (6): 1126- 1135
3	Huang J Z , Fu C H . Oscillation criteria of generalized Emden-Fowler equations. Acta Mathematicae Applicatae Sinica, 2015, 38 (6): 1126- 1135
4	曾云辉, 罗李平, 俞元洪. 中立型Emden-Fowler时滞微分方程的振动性. 数学物理学报, 2015, 35A (4): 803- 814
4	Zeng Y H , Luo L P , Yu Y H . Oscillation for Emden-Fowler delay differential equations of neutral type. Acta Mathematica Scientia, 2015, 35A (4): 803- 814
5	李文娟, 汤获, 俞元洪. 中立型Emden-Fowler微分方程的振动性. 数学物理学报, 2017, 37A (6): 1062- 1069
5	Li W J , Tang H , Yu Y H . Oscillation of the neutral Emden-Fowler differential equation. Acta Mathematica Scientia, 2017, 37 (6): 1062- 1069
6	Xing G J , Li T X , Zhang C H . Oscillation of higher-order quasi-linear neutral differential equations. Advances in Difference Equations, 2011, 2011: 45
7	杨甲山, 方彬. 二阶广义Emden-Fowler型微分方程的振荡性. 华中师范大学学报(自然科学版), 2016, 50 (6): 799- 804
7	Yang J S , Fang B . Oscillation of certain second-order generalized Emden-Fowler-type differential equations. Journal of Central China Normal University (Natural Sciences), 2016, 50 (6): 799- 804
8	杨甲山. 二阶Emden-Fowler型非线性变时滞微分方程的振荡准则. 浙江大学学报(理学版), 2017, 44 (2): 144- 149
8	Yang J S . Oscillation criteria of second-order Emden-Fowler nonlinear variable delay differential equations. Journal of Zhejiang University (Science Edition), 2017, 44 (2): 144- 149
9	Sun S R , Li T X , Han Z L , et al. On oscillation of second-order nonlinear neutral functional differential equations. Bull Malays Math Sci Soc, 2013, 36 (3): 541- 554
10	Ye L , Xu Z . Oscillation criteria for second order quasilinear neutral delay differential equations. Applied Mathematics and Computation, 2009, 207 (2): 388- 396
11	罗红英, 屈英, 俞元洪. 具有正负系数的二阶中立型时滞Emden-Fowler方程的振动准则. 应用数学学报, 2017, 40 (5): 667- 675
11	Luo H Y , Qu Y , Yu Y H . Oscillation criteria of second order neutral delay Emden-Fowler equations with positive and negative coefficients. Acta Mathematicae Applicatae Sinica, 2017, 40 (5): 667- 675
12	杨甲山. 一类具有非线性中立项的二阶微分方程振动性. 东北师大学报(自然科学版), 2017, 49 (3): 13- 17
12	Yang J S . Oscillation of certain second-order differential equations with nonlinear neutral term. Journal of Northeast Normal University (Natural Science Edition), 2017, 49 (3): 13- 17

[1]	胡冰冰, 高建芳. 一类具有变系数的非线性延迟微分方程数值解的振动性分析[J]. 数学物理学报, 2025, 45(1): 203-213.
[2]	何亚兴, 唐应辉, 刘琼琳. 修理设备可更换的${N}$ -策略延迟不中断单重休假 ${M/G/1}$可修排队系统分析[J]. 数学物理学报, 2023, 43(2): 625-645.
[3]	刘莹,高建芳. 一类自变量分段连续系统的振动性分析[J]. 数学物理学报, 2022, 42(3): 826-838.
[4]	张萍,杨甲山,覃桂茳. 时间轴上二阶非线性非自治延迟动力系统的振动性[J]. 数学物理学报, 2022, 42(3): 839-850.
[5]	覃桂茳,杨甲山. 具拟线性中立项的二阶变时滞动力方程的振动定理[J]. 数学物理学报, 2021, 41(5): 1492-1503.
[6]	仉志余. 具次线性中立项的二阶广义Emden-Fowler时滞微分方程的振动准则[J]. 数学物理学报, 2021, 41(3): 811-826.
[7]	张萍,杨甲山. 时标上具非正中立项的二阶动力方程的动力学性质[J]. 数学物理学报, 2021, 41(1): 217-226.
[8]	李继猛,杨甲山. 具非线性中立项的二阶延迟微分方程的Philos型准则[J]. 数学物理学报, 2020, 40(1): 169-186.
[9]	张晓晓,董华. 具有借贷利率的经典模型的Parisian分红问题[J]. 数学物理学报, 2019, 39(5): 1272-1280.
[10]	张万路, 殷晓龙, 赵翔华. 对偶延迟更新风险模型的占位时[J]. 数学物理学报, 2019, 39(4): 918-931.
[11]	仉志余,俞元洪,李淑萍,乔士柱. 二阶非线性中立型时滞微分方程的振动性[J]. 数学物理学报, 2019, 39(4): 797-811.
[12]	张根根,王晚生,肖爱国. 一类变延迟中立型微分方程梯形方法的渐近估计[J]. 数学物理学报, 2019, 39(3): 560-569.
[13]	张万路,赵翔华. 折射Lévy风险过程的Parisian破产问题[J]. 数学物理学报, 2019, 39(1): 184-199.
[14]	潘取玉,唐应辉. 在延迟Min (N, D)-策略M/G/1可修排队系统及最优控制策略[J]. 数学物理学报, 2018, 38(5): 1014-1031.
[15]	王慧灵, 高建芳. 一类带有多项延迟的非线性中立型延迟微分方程解析解的振动性分析[J]. 数学物理学报, 2018, 38(4): 740-749.