A topological approach to periodic oscillations related to the Liebau   phenomenon
  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. 
Jos\'e \'Angel Cid, Gennaro Infante, Milan Tvrd\'y and Miros{\l}awa   Zima
math.CA