三阶非线性中立型微分方程的振动性和渐近性  

Oscillatory and Asymptotic Behavior of Third-order Nonlinear Neutral Differential Equations

作　　者：曾云辉 罗李平 俞元洪[2] ZENG YUNHUI;LUO LIPING;YU YUANHONG(College of Mathematics and Statistics,Hengyang Normal University,Hengyang,Hunan 421002,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]衡阳师范学院数学与统计学院,衡阳421002 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《应用数学学报》2021年第4期508-521,共14页Acta Mathematicae Applicatae Sinica

基　　金：湖南省自然科学基金项目(2019JJ40004);湖南省教育厅科学基金重点项目(20A063);湖南省双一流应用特色学科项目(湘教通[2018]469);湖南省科技创新计划项目(2016TP1020)资助。

摘　　要：本文的目的是研究三阶非线性中立型连续分布时滞微分方程(τ(t)[(x)t)+∫_(a)^(b)p(t,ξ)x(τ(t,ξ))dξ)″]^(a))′+∫_(c)^(d)q(tξ)f(x(σ(t,ξ)))dξ=0解的振动性和渐近性,其中f(x)/x^(β)≥δ>0,x≠0且α>0和β>0均为正奇数之商.利用广义Riccati变换和积分平均技巧,我们对α≠β的情况,建立了一组保证方程每一解振动或者收敛到零的充分条件,所得结果改进和推广了最新文献中的一些熟知的准则,说明新结果应用的若干例子也被给出.The objective of this paper is to study oscillatory and asymptotic behaviors of solutions of a class of third-order nonlinear neutral differential equations with continuously distributed delay(τ(t)[(x)t)+∫_(a)^(b)p(t,ξ)x(τ(t,ξ))dξ)″]^(a))′+∫_(c)^(d)q(tξ)f(x(σ(t,ξ)))dξ=0where f(x)/xβ≥δ>0,x≠0,α>0 andβ>0 are the quotient of positive odd number.By using generalized Riccati transformations and integral averaging technique,we establish a set of new sufficient conditions forα≠βwhich ensure that every solution of the equations oscillates or converges to zero.Our results improve and extend related criteria in the literature,recently.Examples are provided to illustrate new results.

关 键 词：振动 渐近性 三阶中立型微分方程 广义Riccati变换 

分 类 号：O175.27[理学—数学]