具有振动强迫项的二阶中立型阻尼泛函微分方程渐近性  

Asymptotic Behavior of Second-order Neutral Damped Functional Differential Equations with Forced Oscillation

作　　者：韩忠月[1] 吴玉杰[1] 孔淑霞[1] 高秀娟[1] HAN Zhong-yue;WU Yu-jie;KONG Shu-xia;GAO Xiu-juan(School of Mathematics and Big Data,Dezhou University,Dezhou Shandong 253023,China)

机构地区：[1]德州学院数学与大数据学院,山东德州253023

出　　处：《德州学院学报》2022年第4期1-9,共9页Journal of Dezhou University

基　　金：山东省自然科学基金(项目编号:ZR2017LA012)。

摘　　要：利用广义的黎卡提变换和算术几何平均不等式,结合积分性质对具有振动强迫项的二阶中立型阻尼泛函微分方程的振动与渐近性进行了研究,获得了该类方程存在振动解的若干充分条件,探讨了一类微分方程的强迫项在方程解的渐近性质中的作用,改进和推广了已有文献的结果,给出了具体的应用实例。By using the generalized Riccati transformation and arithmetic geometric mean inequality combined with the Integral properties,the oscillation and Asymptotic Behavior of second order half-linear neutral damped functional differential equations with forced oscillation is studied.First of all,some new sufficient conditions for oscillation of all solutions of the equations are obtained.Secondly,the effect of the forced oscillation on the asymptotic properties of the solution of a class of differential equations is discussed,which improved and generalized the results in the literature.And lastly,several examples are given to illustrate the applications of the obtained results.

关 键 词：半线性中立型 泛函微分方程 振动准则 渐近性质 阻尼 强迫振动 

分 类 号：O175.2[理学—数学]