一类三阶时滞微分方程的正周期解  

Positive Periodic Solutions of a Class of Third-Order Differential Equations with Delays

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：《吉林大学学报（理学版）》2022年第6期1285-1291,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061062;11661071)。

摘　　要：考虑三阶多时滞常微分方程u(t)+a(t)u(t)=f(t,u(t-τ1),…,u(t-τn)),t∈R正2π-周期解的存在性,其中:系数函数a:R→(0,+∞)连续,关于t以2π为周期;非线性项f:R×[0,+∞)n→[0,+∞)连续,关于t以2π为周期;τ_(1),τ_(2),…,τ_(n)为正常数.在允许非线性项f(t,x_(1),x_(2),…,x n)关于x_(1),x_(2),…,x_(n)超线性或次线性增长的不等式条件下,利用锥上的不动点指数理论给出该问题正2π-周期解的存在性结果.We consider the existence of positive 2π-periodic solutions of the third-order ordinary differential equations with multiple delays u(t)+a(t)u(t)=f(t,u(t-τ1),…,u(t-τn)),t∈R,where coefficient function a:R→(0,+∞)is continuous,and the period of t is 2π,nonlinear term f:R×[0,+∞)_(n)→[0,+∞)is continuous,and the period of t is 2π,andτ_(1),τ_(2),…,τ_(n) are positive constants.Using fixed point index theory in cones,we give the existence results of positive 2π-periodic solutions of the problem under the inequality conditions that allow the nonlinear term f(t,x _(1),x_(2),…,x_(n))to grow superlinearly or sublinearly on x_(1),x_(2),…,x_(n).

关 键 词：时滞 三阶常微分方程 正周期解 锥 不动点指数 

分 类 号：O175.8[理学—数学]