Positive periodic solutions of singular systems of first order ordinary differential equations

TL;DR

This paper investigates the existence and multiplicity of positive periodic solutions in singular first-order differential systems, using fixed point theory under superlinear or sublinear conditions at infinity.

Contribution

It introduces new conditions for positive periodic solutions in singular systems and applies Krasnoselskii's fixed point theorem in a novel way.

Findings

Established conditions for existence of solutions

Proved multiplicity results under certain assumptions

Applied fixed point theorem to singular systems

Abstract

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone.