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New results for the Liebau phenomenon via fixed point index |
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| Institution: | 1. Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China;2. Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Taiyuan 030006, Shanxi, China;1. Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy;2. DIST, Politecnico di Torino, Viale Mattioli 39, 10125 Torino, Italy;3. CMAT, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal;4. Dipartimento di Matematica “F. Enriques”, Università di Milano, via Cesare Saldini 50, 20133 Milano, Italy |
| 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. |
| Keywords: | Valveless pumping Periodic boundary value problem Cone Fixed point index Green’s function |
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