摘要
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
本文给出带有不定奇性的微分方程x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t)的周期正解存在的充分条件.其中,ρ和δ为两个正常数且0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)为正函数.我们的证明基于不动点定理(Schauder不动点定理和Krasnoselskii-Guo不动点定理)以及相关Green函数的正性.
出处
《数学理论与应用》
2025年第1期81-93,共13页
Mathematical Theory and Applications
基金
supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)
the Natural Science Foundation of Henan Province(No.222300420449)
the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
