一类三阶中立型时滞微分方程周期解的存在性  

Existence of the periodic solutions for a class of third-order neutral differential equations with delay

作　　者：杨生斌 李永祥 YANG Shengbin;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《黑龙江大学自然科学学报》2022年第5期505-512,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(12061062,11661071)。

摘　　要：利用上下解的单调迭代技巧,讨论了三阶中立型时滞微分方程(u(t)-cu(t-δ))′′′=f(t,u(t),u(t-τ)),t∈R的2π-周期解的存在性,其中δ>0,|c|<1为常数,f:R×R×R→R连续,关于t以2π为周期,τ为正常数。通过正算子扰动的方法和建立新的极大值原理,构造了上述方程的2π-周期解的单调迭代求解程序,获得了该方程的2π-周期解的存在性与唯一性结果。Using the technique of monotone iterative of upper and lower solutions,the existence problem of 2π-periodic solutions for the third-order neutral differential equations with delay (u(t)-cu(t-δ))′′′=f(t,u(t),u(t-τ)),t∈Ris discussed,where δ>0,|c|<1 are constants,f:R×R×R→R is a continuous function in which t is 2πperiodic andτis positive constant.By method of positive operator perturbation and establishing a new maximum principle,a monotone iterative procedure is constructed to seek the 2π-periodic solutions of the equations and the existence and uniqueness results of 2π-periodic solutions are obtained.

关 键 词：中立型微分方程 时滞 周期性 单调迭代方法 

分 类 号：O175.15[理学—数学]