华东师范大学学报（自然科学版） >

2019 , Vol. 2019 >Issue 4: 11 - 18

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.04.002

数学

二阶广义Emden-Fowler型微分方程的振荡性

  • 李继猛
展开
  • 邵阳学院 理学院, 湖南 邵阳 422004
李继猛,男,副教授,研究方向为微分方程的理论及解析不等式.E-mail:syxyljm@163.com.

收稿日期: 2018-05-05

  网络出版日期: 2019-07-18

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）

收起

Oscillation of second-order generalized Emden-Fowler-type differential equations

  • LI Ji-meng
Expand
  • School of Science, Shaoyang University, Shaoyang Hunan 422004, China

Received date: 2018-05-05

  Online published: 2019-07-18

Fold

摘要

研究了一类二阶广义Emden-Fowler型非线性变时滞中立型泛函微分方程的振荡性.利用广义Riccati变换技术及一些分析技巧，在条件∫t0+∞ a-1/β（t）dt<+∞下建立了该类方程振荡的两个新的判别准则.所举例子说明，这些准则不仅推广和改进了一些已有的结果，而且具有较好的实用性和可操作性.

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

本文引用格式

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 . DOI: 10.3969/j.issn.1000-5641.2019.04.002

Abstract

The oscillatory behavior of a class of second-order generalized EmdenFowler-type nonlinear variable delay neutral functional differential equations is studied in this article. By using the generalized Riccati transformation and some analytic techniques, we establish two new oscillation criteria for the equations under the condition ∫t0+∞ a-1/β(t)dt<+∞. Illustrative examples are provided to show that our results extend and improve those previously reported in the literature, and the results are both practical and implementable.

Key words： oscillation; Emden-Fowler-type differential equation; Riccati transformation

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] 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.
[3] 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.
[4] 杨甲山, 方彬. 二阶广义Emden-Fowler型微分方程的振荡性[J]. 华中师范大学学报(自然科学版), 2016, 50(6):799-804.
[5] 曾云辉, 罗李平, 俞元洪. 中立型Emden-Fowler时滞微分方程的振动性[J]. 数学物理学报(A辑), 2015, 35(4):803-814.
[6] LI T X, ROGOVCHENKO Y V. Oscillatory behavior of second-order nonlinear neutral differential equations[J]. Abstract and Applied Analysis, 2014:1-8. doi:10.1155/2014/143614.
[7] 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.
[8] YANG J S, WANG J J, QIN X W, et al. Oscillation of nonlinear second-order neutral delay differential equations[J]. Journal of Nonlinear Sciences and Applications, 2017, 10(5):2727-2734.
[9] 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.
[10] 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[J].应用数学学报, 2017, 40(5):667-675.
Options
文章导航

/

〈 〉