New results for the Liebau phenomenon via fixed point index
Jos\'e \'Angel Cid, Gennaro Infante, Milan Tvrd\'y, Miros{\l}awa, Zima
TL;DR
This paper establishes new existence results for positive solutions in a nonlinear periodic boundary value problem related to the Liebau phenomenon, using fixed point index methods, and provides conditions for a pump in a model.
Contribution
It introduces novel sufficient conditions for solutions and pump existence, improving and complementing previous research using classical fixed point index techniques.
Findings
New sufficient conditions for positive solutions
Conditions for the existence of a pump in the model
Examples illustrating the theoretical results
Abstract
We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature.
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