显含阻尼项的二阶非线性中立型Emden-Fowler微分方程的振动性和渐近性  

Oscillation and Asymptotic Behavior for Second OrderNonlinear Neutral Emden-Fowler Differential Equations withExplicit Damping

作　　者：仉志余 宋菲菲 俞元洪[2] ZHANG Zhiyu;SONG Feifei;YU Yuanhong(Department of Science,Taiyuan Institute of Technology,Taiyuan 030008,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]太原工业学院理学系,山西太原030008 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《应用数学》2020年第3期770-781,共12页Mathematica Applicata

基　　金：国家自然科学基金(11701528,11647034);山西省自然科学基金(2011011002-3)。

摘　　要：本文研究一类带有更广泛而又不失物理意义阻尼项的二阶非线性中立型Emden-Fowler时滞微分方程的振动性和渐近性.利用指数变换、Riccati变换和不等式技巧,获得该类方程几个新的振动准则,推广、改进和统一已有文献中的研究成果,并逐一给出例子说明了相应定理的实用效果.In this paper,by using the methods of exponential function transformation,Riccati transformation and inequality techniques,we study the oscillation and asymptotic behavior for a class of second order nonlinear neutral delay Emden-Fowler differential equations with the wider range and without losing physical meaning damping terms.Several new oscillation criteria which extend and improve some known results in the literature recently are established and some examples are provided to illustrate the effect of new theorems.

关 键 词：振动准则 渐近性 EMDEN-FOWLER方程 中立型非线性微分方程 二阶 阻尼项 

分 类 号：O175.12[理学—数学]