New results for the Liebau phenomenon via fixed point index
  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. 
Jos\'e \'Angel Cid, Gennaro Infante, Milan Tvrd\'y and Miros{\l}awa   Zima
math.CA