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  

Oscillation Criteria of Second-Order Generalized Emden-Fowler Delay Differential Equations with a Sub-Linear Neutral Term

作　　者：仉志余 Zhang Zhiyu(Department of Sciences,Taiyuan Institute of Technology,Taiyuan 030008)

机构地区：[1]太原工业学院理学系,太原030008

出　　处：《数学物理学报（A辑）》2021年第3期811-826,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701528,11747098);山西省自然科学基金(2011011002-3)。

摘　　要：该文研究一类具有次线性中立项的二阶广义Emden-Fowler型时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程较简便的多个新振动准则,所得准则推广和改进了近年来已有的包括适应于Euler方程的经典研究成果.最后,该文还构造实例验证了所得振动准则的广泛应用效果.In this paper,we study the oscillation of second order generalized Emden-Fowler delay differential equations with a sub-linear neutral term.Under the irregularity condition,by using Riccati transformation and the inequalities technique,several simple new oscillation criteria of this kind of equations to ensure that every solution oscillates are established.These oscillation criteria generalize and improve the classical research results including those adapted to Euler equations established in previous literatures.Finally,some examples to verify the wide application of these oscillation criteria are given in this paper.

关 键 词：EMDEN-FOWLER方程 EULER方程 二阶 时滞微分方程 次线性中立项 振动准则 RICCATI变换 

分 类 号：O175[理学—数学]