含时滞导数项的高阶常微分方程的正周期解

doi:10.6040/j.issn.1671-9352.0.2018.258

摘要/Abstract

摘要： 研究了非线性项中含有时滞导数项的高阶常微分方程u⁽ⁿ⁾(t)+a(t)u(t)=f(t, u(t-τ₀(t)), u'(t-τ₁(t)),…, u^(n-1)(t-τ_n-1(t))), t∈R正 ω-周期解的存在性, 其中 n≥2, a:R→(0,∞)连续以 ω 为周期, f:R×［0,∞)×R^n-1→［0,∞)连续, 关于t以ω为周期, τ_k:R→［0,∞)连续以ω为周期, k=0,1,…,n-1。运用正算子扰动方法和锥上的不动点指数理论, 获得了该方程正 ω-周期解的存在性结果。

关键词: 时滞微分方程, 正周期解, 锥, 不动点指数

Abstract: This paper deals with the existence of positive ω-periodic solutions for the higher-order ordinary differential equation with delayed derivative terms in nonlinearityu⁽ⁿ⁾(t)+a(t)u(t)=f(t, u(t-τ₀(t)), u'(t-τ₁(t)),…, u^(n-1)(t-τ_n-1(t))), t∈R,where n≥2, a:R→(0,∞)is a continuous function which is ω-periodic, f:R×［0,∞)×R^n-1→［0,∞)is a continuous function which is ω-periodic on t, and τ_k:R→［0,∞)is a continuous function which is ω-periodic, k=0,1,…,n-1. By using the perturbation method of positive operator and fixed point index theory in cones, we obtain the existence results of positive ω-periodic solutions for the equation.

Key words: differential equation with delay, positive periodic solution, cone, fixed point index

中图分类号:

O175.15

章欢,李永祥. 含时滞导数项的高阶常微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(4): 29-36.

ZHANG Huan, LI Yong-xiang. Positive periodic solutions of higher-order ordinary differential equations with delayed derivative terms[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 29-36.

参考文献

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