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).
作者
杨生斌
李永祥
YANG Shengbin;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)
出处
《吉林大学学报（理学版）》
CAS
北大核心
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)。
关键词
时滞
三阶常微分方程
正周期解
锥
不动点指数
delay
third-order ordinary differential equation
positive periodic solution
cone
fixed point index
