Positive periodic solutions of singular systems

TL;DR

This paper investigates the existence and multiplicity of positive periodic solutions in second order non-autonomous singular dynamical systems, using fixed point theory to unify and improve previous results.

Contribution

It introduces a unified approach employing Krasnoselskii fixed point theorem to establish positive solutions under superlinear or sublinear conditions, advancing the theoretical understanding.

Findings

Established conditions for existence of solutions.

Proved multiplicity results for certain parameter ranges.

Unified treatment improves upon previous literature.

Abstract

The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our results provide a unified treatment for the problem and significantly improve several results in the literature. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone.