A topological approach to periodic oscillations related to the Liebau phenomenon

TL;DR

This paper introduces a topological method using Krasnosel'ski-Guo theorem to analyze the existence and localization of positive solutions in periodic boundary value problems related to the Liebau phenomenon, improving previous results.

Contribution

It provides new sufficient conditions for solutions of the Liebau-related boundary value problem using a topological approach, enhancing existing theoretical frameworks.

Findings

Established conditions for existence of positive solutions.

Identified criteria for non-existence of solutions.

Localized solutions under certain parameter regimes.

Abstract

We give some sufficient conditions for existence, non-existence and localization of positive solutions for a periodic boundary value problem related to the Liebau phenomenon. Our approach is of topological nature and relies on the Krasnosel'ski\u\i{}-Guo theorem on cone expansion and compression. Our results improve and complement earlier ones in the literature.