具非线性中立项的二阶变时滞微分方程的振荡性

doi:10.3969/j.issn.1000-5641.2016.04.004

华东师范大学学报(自然科学版)

具非线性中立项的二阶变时滞微分方程的振荡性

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

收稿日期:2015-09-11 出版日期:2016-07-25 发布日期:2016-09-29
通讯作者: 杨甲山, 男, 教授, 研究方向为微分方程的理论及应用. E-mail: syxyyjs@163.com.
基金资助:
广西教育厅科研基金项目 (2013YB223) ; 国家青年科学基金项目 (61503171); 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)

Oscillation of second-order variable delay differential equations with nonlinear neutral term

YANG Jia-shan^[1,2]

1. School of Information and Electronic Engineering, Wuzhou University, Wuzhou Guangxi 543002, China;
2. Laboratory of Complex Systems Simulation and Intelligent Computing, Wuzhou University, Wuzhou Guangxi 543002, China

Received:2015-09-11 Online:2016-07-25 Published:2016-09-29

摘要/Abstract

摘要：

研究了一类具有一个非线性中立项的二阶变时滞非线性泛函微分方程的振荡性.利用 Riccati 变换技术及一些分析技巧, 获得了该类方程振荡的两个新判别准则, 这些准则推广且改进了现有文献中的一些结果.

关键词: 振荡性 , 变时滞 , 泛函微分方程 , 非线性中立项 , Riccati 变换

Abstract:

We study the oscillatory behavior of a certain class of second-order variable delay nonlinear functional differential equations with a nonlinear neutral term in this article. By using the generalized Riccati transformation and some necessary analytic techniques, we establish two new oscillation criteria for the oscillation of the equations. In particular, the results obtained improve those presented in the literature.

Key words: oscillation, variable delay, functional differential equation, nonlinear neutral term, Riccati transformation

杨甲山. 具非线性中立项的二阶变时滞微分方程的振荡性[J]. 华东师范大学学报(自然科学版), doi: 10.3969/j.issn.1000-5641.2016.04.004.

YANG Jia-shan. Oscillation of second-order variable delay differential equations with nonlinear neutral term[J]. Journal of East China Normal University(Natural Sc, doi: 10.3969/j.issn.1000-5641.2016.04.004.

参考文献

[ 1 ] AGARWAL R P, BOHNER M, LI W T. Nonoscillation and Oscillation: Theory for Functional Differential
Equations [M]. New York: Marcel Dekker, 2004.
[ 2 ] BACUL´IKOV´A B, D ? ZURINA J. Oscillation theorems for second order neutral differential equations [J]. Comput
Math Appl, 2011, 61: 94-99.
[ 3 ] HASANBULLI M, ROGOVCHENKO YU V. Oscillation criteria for second order nonlinear neutral differential
equations [J], Appl Math Comput, 2010, 215: 4392-4399.
[ 4 ] LI T, AGARWAL R P, BOHNER M. Some oscillation results for second-order neutral differential equations [J].
J Indian Math Soc, 2012, 79: 97-106.
[ 5 ] LI T, AGARWAL R P, BOHNER M. Some oscillation results for second-order neutral dynamic equations [J].
Hacet J Math Stat, 2012, 41: 715-721.
[ 6 ] LI T X, HAN Z L, ZHANG C H, et al. Oscillation criteria for second-order superlinear neutral differential
equations [J]. Abstr Appl Anal, 2011 (1): 1-17.
[ 7 ] LI T X, HAN Z L, ZHANG C H, et al. On the oscillation of second-order Emden-Fowler neutral differential
equations [J]. J Appl Math Computing, 2011, 37: 601-610.
[ 8 ] LI T X, ROGOVCHENKO Y V, ZHANG C H. Oscillation of second-order neutral differential equations [J].
Funkc Ekvac, 2013, 56: 111-120.
[ 9 ] LIN X, TANG X. Oscillation of solutions of neutral differential equations with a superlinear neutral term [J].
Appl Math Lett, 2007, 20: 1016-1022.
[10] HAN Z L, LI T X, SUN S R, et al. Remarks on the paper [Appl. Math. Comput. 207 (2009) 388-396] [J]. Appl
Math Comput, 2010, 215(11): 3998-4007.
[11] LI T X, ROGOVCHENKO Y V. Oscillation theorems for second-order nonlinear neutral delay differential equa-
tions [J]. Abstract and Applied Analysis, 2014, 2014: 1-6.
[12] SUN S, LI T X, HAN Z L, et al. Oscillation theorems for second-order quasilinear neutral functional differential
equations [J]. Abstract and Applied Analysis, 2012, 2012: 1-17.
[13] 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, 2012: 227.
[14] 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.
[15] 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, 2015: 97.
[16] 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.
[17] AGARWAL R P, BOHNER M, LI T X, et al. Oscillation of second-order differential equations with a sublinear
neutral term [J]. Carpathian Journal of Mathematics, 2014, 30(1): 1-6.
[18] 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, 2015(3): 9-15.
[19] 杨甲山, 孙文兵. 一类多时滞二阶中立型微分方程的振动性~[J]. 中北大学学报 (自然科学版), 2012, 33(4): 363-368.
[20] 杨甲山, 方彬. 一类二阶中立型微分方程的振动和非振动准则~[J]. 四川师范大学学报 (自然科学版), 2012, 35(6): 776-780.
[21] 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.
[22] 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.
[23] 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.

[1]	刘锦, 赵维锐. 具有时变时滞的中立型神经网络的稳定性分析[J]. 华东师范大学学报（自然科学版）, 2020, 2020(4): 35-44.
[2]	李继猛. 二阶广义Emden-Fowler型微分方程的振荡性[J]. 华东师范大学学报(自然科学版), 2019, 2019(4): 11-18.
[3]	杨甲山, 张晓建. 时间模上一类二阶非线性动态方程振荡性的新结果[J]. 华东师范大学学报(自然科学版), 2017, (3): 54-63.
[4]	李默涵. 时间尺度上一类三阶变时滞阻尼动态方程的振荡性(英)[J]. 华东师范大学学报(自然科学版), 2016, 2016(4): 11-24.
[5]	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, 2015(3): 9-15.
[6]	杨甲山. 时间测度链上二阶动力方程的振动准则[J]. 华东师范大学学报(自然科学版), 2012, 2012(3): 17-23.
[7]	许建强;;陈树中. 变时滞互联项不确定大系统的分散自适应控制 (英)[J]. 华东师范大学学报(自然科学版), 2007, 2007(5): 98-106.
[8]	许建强;陈树中;. 含时滞扰动非线性系统的输出反馈自适应控制[J]. 华东师范大学学报(自然科学版), 2006, 2006(3): 60-65.
[9]	张晓霞. 一类二阶时滞微分方程解的振荡性、有界性和单调性[J]. 华东师范大学学报(自然科学版), 2005, 2005(5/6): 79-84,1.

具非线性中立项的二阶变时滞微分方程的振荡性

Oscillation of second-order variable delay differential equations with nonlinear neutral term

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

编辑推荐

Metrics

本文评价