含参系统正周期解的存在性及多解性

doi:10.12677/PM.2021.111017

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含参系统正周期解的存在性及多解性
Existence and Multiplicity of Positive Periodic Solutions for Systemswith Parameters

DOI: 10.12677/PM.2021.111017, PDF, HTML, 下载: 398 浏览: 2,496 国家自然科学基金支持
作者: 杨伟：西北师范大学数学与统计学院，甘肃兰州
关键词: 正解；多解；含参；Positive Solutions； Multiple Solutions； Parametric

摘要: 本文考察含参系统

其中，λ是一个正参数，a,b:[0,1]→[0,∞)是连续函数且a,b在[0,1]的任意子区间上不恒为零，f,g:[0,1]×[0,∞)×[0,∞)→[0,∞)是连续函数。本文基于Krasnoselskill不动点定理得到了一阶常微分系统的无穷多个正周期解。

Abstract: In this paper, we consider systems with parameters

where λ is a positive parameter, a, b : [0,1] → [0,∞) are continuous function and do not vanish identically on any subinterval of [0,1], f, g : [0,1] × [0,∞) × [0,∞) → [0,∞) are continuous function. In this paper, based on the Krasnoselskill fixed point theorem, an infinite number of positive periodic solutions for systems with parameters.

文章引用：杨伟. 含参系统正周期解的存在性及多解性[J]. 理论数学, 2021, 11(1): 115-125. https://doi.org/10.12677/PM.2021.111017

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