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

Abstract

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). $$ x'''+a(t)x=f(t,x)+e(t). $$ 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.

Keywords

• Singular differential equations
• Positive periodic solutions
• Variable coefficients
• Constant coefficients
• Green’s function