带弱奇异项的二阶微分方程正周期解的存在性（英文）

Existence of positive periodic solutions of second-order differential equation with weak singularity

本文运用Schauder不动点定理获得了一类二阶非线性微分方程u″+a(t)u=f(t,u)+c(t)正周期解的存在性,其中a∈L^1(R/TZ;R+),c∈L^1(R/TZ;R),f为Carathéodory函数.本文的主要结果推广了一些已有结果.

The existence of positive periodic solutions of the following second-order differential equation u″+a(t)u=f(t,u)+c(t)is considered via Schauder s fixed point theorem,where a∈L 1(R/T Z;R+),c∈L 1(R/T Z;R),f is a Carathéodory function.Our main results generalize some known results.