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

摘要/Abstract

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.

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

Abstract:

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.

Key words: Emden-Fowler equation, Euler equation, Second order, Delay differential equation, Sub-linear neutral term, Oscillation criterion, Riccati transformation

中图分类号:

O175

仉志余. 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[J]. 数学物理学报, 2021, 41(3): 811-826.

Zhiyu Zhang. Oscillation Criteria of Second-Order Generalized Emden-Fowler Delay Differential Equations with a Sub-Linear Neutral Term[J]. Acta mathematica scientia,Series A, 2021, 41(3): 811-826.

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