Mirosława Zima

A TOPOLOGICAL APPROACH TO PERIODIC OSCILLATIONS RELATED TO THE LIEBAU PHENOMENON

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 Krasnoselskiĭ–Guo theorem on cone expansion and compression. Our results improve and complement earlier ones in the literature.

On the Darboux problem of neutral type

The aim of this paper is to prove uniqueness theorems for the Darboux problem of neutral type in the space L ∞ and L 1 .

New results for the Liebau phenomenon via fixed point index

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.