The aim of this paper is to show that fixed point theorem in cones can be applied to singular equations. Using the positivity of Green’s function and the external force e(t), we prove the existence of a positive periodic solution for a damped singular equation with sub-linearity, semi-linearity and super-linearity conditions, and these results are applicable to weak and strong singularities. As applications, we consider the existence of a positive periodic solution for nonlinear elasticity model and Ermakov–Pinney equation

中文翻译：

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锥上不动点定理的二阶阻尼奇异方程的正周期解

本文的目的是证明圆锥中的不动点定理可以应用于奇异方程。利用格林函数的正性和外力e（t），我们证明了具有亚线性，半线性和超线性条件的阻尼奇异方程的正周期解的存在，并且这些结果适用于弱和强烈的奇点。作为应用，我们考虑非线性弹性模型和Ermakov-Pinney方程的正周期解的存在