具非线性中立项的二阶延迟微分方程的Philos型准则  

Philos-Type Criteria for Second-Order Delay Differential Equations with Nonlinear Neutral Term

作　　者：李继猛 杨甲山 Li Jimeng;Yang Jiashan(School of Science,Shaoyang University,Hunan Shaoyang 422004;School of Data Science and Software Engineering,Wuzhou University,Guangxi Wuzhou 543002)

机构地区：[1]邵阳学院理学院,湖南邵阳422004 [2]梧州学院大数据与软件工程学院,广西梧州543002

出　　处：《数学物理学报（A辑）》2020年第1期169-186,共18页Acta Mathematica Scientia

基　　金：国家自然科学基金项目(51765060);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)。

摘　　要：利用黎卡提变换技术,结合伯努利、杨氏不等式以及数学分析技巧,研究了具有非线性中立项的Emden-Fowler型微分方程{a(t)|[x(t)+p(t)x^α(τ(t))]′|^β-1[x(t)+p(t)x^α(τ(t))]′}′+q(t)f(|x(δ(t))|^γ-1x(δ(t)))=0,t≥t0的振动性,获得了该方程的若干新Philos型振动定理,所举例子说明,这些准则不仅推广并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.We study the oscillatory behavior of Emden-Fowler-type differential equations with a nonlinear neutral term{a(t)|[x(t)+p(t)x^α(τ(t))]′|^β?1[x(t)+p(t)x^α(τ(t))]′}′+q(t)f(|x(δ(t))|^γ?1x(δ(t)))=0,t≥t0 in this article.By using the generalized Riccati transformation,and Bernoulli inequality,Yang inequality and integral averaging technique,we establish some new oscillation criterions for the equations.The illustrative examples are provided to show that our results obtained extend and improve those reported in the literature,and have practicability and maneuverability.

关 键 词：振动性 Emden-Fowler型微分方程 非线性中立项 RICCATI变换 

分 类 号：O175.1[理学—数学]