Study on variable coefficients singular differential equation via constant coefficients differential equation

Abstract

In this paper, we consider the following third-order singular differential equation with variable coefficients: x + a(t)x = f (t, x) + e(t). By using the Green's function of the linear differential equation with constant coefficients and some fixed point theorems, i.e., Leray-Schauder alternative principle and Schauder's fixed point theorem, we prove the existence of positive periodic solutions of the above equation.