一类无界时滞微分方程解振动的判定  

Some Sufficient and Necessary Conditions for the Oscillation of All Solutions of a Class of Differential Equations with Unbounded Delays

作　　者：席军 关开中 旷菊红[1] XI Jun;GUAN Kai-zhong;KUANG Ju-hong(School of Mathematics and Computational Science,Wuyi University,Jiangmen 529020,China)

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2018年第3期1-6,共6页Journal of Wuyi University(Natural Science Edition)

基　　金：广东省自然科学基金资助项目(2016A030313005;2015A030313643;2014A030310334)

摘　　要：考虑方程x'(t)+1/tn∑i-1pix(a_it)=0,t≥1,其中p_i∈R,0<a_i<1.通过定义一类新的积分变换并结合分析技巧,得到该方程所有解振动的充分必要条件,推广了已有文献的相关结果,并举例予以说明.This paper considers the equationx'(t)+-1/tΣni-1pix(αit)=0,t≥1,where pi∈R,0﹤αi﹤1,i=1,2···,n.Some sufficient and necessary conditions are established for the oscillation of all solutions of this equation by introducing a new integral transformation and using analysis techniques,some known results in the literature are generalized,and finally two examples are given to illustrate our theoretical results.

关 键 词：时滞微分方程 振动性 无界时滞 积分变换 

分 类 号：O175.12[理学—数学]