Dynamics of periodic second-order equations between an ordered pair of lower and upper solutions

TL;DR

This paper investigates the behavior of periodic second-order differential equations with ordered bounds, demonstrating the existence of trajectories that approach the extremal periodic solutions within those bounds.

Contribution

It establishes the existence of asymptotic trajectories towards maximal and minimal periodic solutions between given lower and upper solutions.

Findings

Existence of asymptotic trajectories towards extremal solutions

Trajectories are bounded between lower and upper solutions

Results apply to a class of periodic second-order equations

Abstract

We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.