Please wait a minute...
浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (2): 144-149    DOI: 10.3785/j.issn.1008-9497.2017.02.004
数学与计算机科学     
二阶Emden-Fowler型非线性变时滞微分方程的振荡准则
杨甲山1,2
1. 梧州学院 信息与电子工程学院, 广西 梧州 543002;
2. 梧州学院 复杂系统仿真与智能计算实验室, 广西 梧州 543002
Oscillation criteria of second-order Emden-Fowler nonlinear variable delay differential equations
YANG Jiashan1,2
1. School of Information and Electronic Engineering, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China;
2. Laboratory of Complex Systems Simulation and Intelligent Computing, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China
 全文: PDF(633 KB)   HTML  
摘要： 研究了一类具有变时滞的二阶Emden-Fowler型非线性中立型泛函微分方程的振荡性.借助Riccati变换、积分平均技术和微分不等式等技巧，获得了该类方程振荡的新判别准则和比较判别定理，推广、改进并丰富了现有文献中的结果.
关键词： 振荡性;  变时滞;  泛函微分方程;  Riccati变换    
Abstract: The purpose of this article is to study the oscillatory behavior of second-order Emden-Fowler nonlinear neutral functional differential equations with variable delay. By using the Riccati transformation, integral averaging technique and differential inequalities, we established a new oscillation criteria and a comparison theorem for the oscillation of the equations. These criteria dealing with some cases have not been covered by the existing results in the literature.
Key words: oscillation    variable delay    functional differential equation    Riccati transformation
收稿日期: 2016-03-26 出版日期: 2017-07-08
CLC:  O175.7  
基金资助: 梧州学院2014年校级科研重大项目（2014A003）；硕士学位授予单位立项建设项目（桂学位[2013]4号）；广西教育厅科研项目（2013YB223）.
作者简介: 杨甲山(1963-),ORCID:http://orcid.org/0000-0002-0340-097X,男,学士,教授,主要从事微分方程的理论与应用研究,E-mail:syxyyjs@163.com.
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　
杨甲山

引用本文:

杨甲山. 二阶Emden-Fowler型非线性变时滞微分方程的振荡准则[J]. 浙江大学学报（理学版）, 2017, 44(2): 144-149.

YANG Jiashan. Oscillation criteria of second-order Emden-Fowler nonlinear variable delay differential equations. Journal of ZheJIang University(Science Edition), 2017, 44(2): 144-149.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.02.004    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I2/144

[1] HASANBULLI M, ROGOVCHENKO Y V. Oscillation criteria for second order nonlinear neutral differential equations[J]. Applied Mathematics and Computation,2010,215(12):4392-4399.
[2] LI T X, AGARWAL R P, BOHNER M. Some oscillation results for second-order neutral differential equations[J]. The Journal of the Indian Mathematical Society,2012,79(1/2/3/4):97-106.
[3] LI T X, AGARWAL R P, BOHNER M. Some oscillation results for second-order neutral dynamic equations[J]. Hacettepe Journal of Mathematics and Statistics,2012,41(5):715-721.
[4] LI T X, ROGOVCHENKO Y V. Oscillatory behavior of second-order nonlinear neutral differential equations[J]. Abstract and Applied Analysis,2014:ID143614.
[5] SUN S R, LI T X, HAN Z L,et al. Oscillation theorems for second-order quasilinear neutral functional differential equations[J]. Abstract and Applied Analysis,2012:ID819342.
[6] ZHANG C H, AGARWAL R P, BOHNER M, et al. New oscillation results for second-order neutral delay dynamic equations[J]. Advances in Difference Equations,2012:227.
[7] ZHONG J,OUYANG Z, ZOU S. An oscillation theorem for a class of second-order forced neutral delay differential equations with mixed nonlinearities[J]. Applied Mathematics Letters,2011,24(8):1449-1454.
[8] AGARWAL R P, BOHNER M, LI T X, et al. A new approach in the study of oscillatory behavior of even-order neutral delay differential equations[J]. Appl Math Comput,2013,225:787-794.
[9] YANG J S, QIN X W. Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales[J]. Advances in Difference Equations,2015:97.Doi:10.1186/S13662-014-0328-X.
[10] YANG J S, QIN X W, ZHANG X J.Oscillation criteria for certain second-order nonlinear neutral delay dynamic equations with damping on time scales[J]. Mathematica Applicata,2015,28(2):439-448.
[11] YE L, XU Z. Oscillation criteria for second order quasilinear neutral delay differential equations[J]. Applied Mathematics and Computation,2009,207(2):388-396.
[12] LI T X, ROGOVCHENKO Y V, ZHANG C H. Oscillation of second-order neutral differential equations[J]. Funkcialaj Ekvacioj,2013,56(1):111-120.
[13] AGARWAL R P, BOHNER M, LI T X, et al. Oscillation of second-order Emden-Fowler neutral delay differential equations[J]. Annali di Matematica Pura ed Applicata,2014,193(6):1861-1875.
[14] 黄记洲,符策红.广义Emden-Fowler方程的振动性[J].应用数学学报,2015,38(6):1126-1135. HUANG J Z, FU C H. Oscillation criteria of generalized Emden-Fowler equations[J]. Acta Mathematicae Applicatae Sinica,2015,38(6):1126-1135.
[15] 杨甲山,方彬.一类二阶中立型微分方程的振动性[J].数学的实践与认识,2013,43(23):193-197. YANG J S, FANG B. Oscillation of a class of second order neutral differential equations[J]. Mathematics in Practice and Theory,2013,43(23):193-197.
[16] 杨甲山.具阻尼项的高阶中立型泛函微分方程的振荡性[J].中山大学学报:自然科学版,2014,53(3):67-72. YANG J S. Oscillation of higher order neutral functional differential equations with damping[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(3):67-72.
[17] 杨甲山.具正负系数和阻尼项的高阶泛函微分方程的振动性[J].华东师范大学学报:自然科学版,2014(6):25-34. YANG J S. Oscillation of higher order functional differential equations with positive and negative coefficients and damping term[J]. Journal of East China Normal University:Natural Science,2014(6):25-34.
[18] XING G J, LI T X, ZHANG C H. Oscillation of higher-order quasi-linear neutral differential equations[J]. Advances in Difference Equations,2011:45.Doi:10.1186/1687-1847-2011-45.
[19] 杨甲山,覃学文.具阻尼项的高阶Emden-Fowler型泛函微分方程的振荡性[J].中山大学学报:自然科学版,2015,54(4):63-68. YANG J S, QIN X W. Oscillation of higher hrder Emden-Fowler functional differential equations with damping[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni,2015,54(4):63-68.
[20] 杨甲山,黄劲.时间模上一类二阶非线性动态方程振荡性的新准则[J].华东师范大学学报:自然科学版,2015(3):9-15. YANG J S, HUANG J. New criteria for oscillation of certain second-order nonlinear dynamic equations on time scales[J]. Journal of East China Nor
[1] 张萍,覃桂茳,杨甲山. 具正负系数和多变时滞的高阶非线性中立型差分方程非振动解的存在性[J]. 浙江大学学报（理学版）, 2022, 49(1): 41-48.
[2] 曾文君, 李德生. 一类带阻尼项非线性分数阶微分方程的振动性[J]. 浙江大学学报（理学版）, 2021, 48(1): 35-40.
[3] 李继猛, 杨甲山. 具非正中立项的二阶非自治延迟动态系统的动力学性质研究[J]. 浙江大学学报（理学版）, 2020, 47(4): 442-447.
[4] 覃桂茳, 刘玉周, 杨甲山. 具正负系数和多变时滞的高阶微分方程的振动性[J]. 浙江大学学报（理学版）, 2020, 47(2): 159-166.
[5] 李继猛, 杨甲山. 时间尺度上二阶拟线性阻尼动力方程的振动性分析[J]. 浙江大学学报（理学版）, 2020, 47(1): 72-76.
[6] 李继猛, 杨甲山. 时间模上一类二阶泛函动态方程振荡的充分条件[J]. 浙江大学学报（理学版）, 2019, 46(4): 405-411.
[7] 李继猛. 时标上二阶广义Emden-Fowler型动态方程的振荡性[J]. 浙江大学学报（理学版）, 2019, 46(3): 309-314.
[8] 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.
[9] 惠远先, 李培峦, 戴丽华. 一类三阶非线性分布时滞动力方程的振动结果[J]. 浙江大学学报（理学版）, 2019, 46(3): 315-322.
[10] 张晓建. 二阶Emden-Fowler型变时滞中立型微分方程的振荡性[J]. 浙江大学学报（理学版）, 2018, 45(3): 308-313.
[11] 张晓建. 时间尺度上一类二阶非线性动力系统的振动性判据[J]. 浙江大学学报（理学版）, 2018, 45(2): 136-142.
[12] 杨甲山, 覃桂茳. 一类二阶微分方程新的Kamenev型振动准则[J]. 浙江大学学报（理学版）, 2017, 44(3): 274-280.
[13] 杨甲山. 具可变时滞的二阶非线性中立型泛函微分方程的振动性[J]. 浙江大学学报（理学版）, 2016, 43(3): 257-263.
[14] 焦建民. 一类区间时变时滞非线性广义系统的稳定性准则[J]. 浙江大学学报（理学版）, 2013, 40(4): 411-415.