A topological approach to periodic oscillations related to the Liebau phenomenon
The authors give some sufficient conditions for existence, non-existence and localization of positive solutions for the periodic boundary value problem \[ x''(t)+ax'(t)=r(t)x^\alpha(t)-s(t)x^\beta(t), x(0)=x(T), x'(0)=x'(T), \] where \(a\geq 0\), \(r\), \(s\in C[0, T]\), \(0<\alpha<\beta <1\). This problem is related to the Liebau phenomenon. Their approach is of topological nature and relies on the Krasnosel'skiǐ-Guo theorem on cone expansion and compression. Their results improve and complement earlier ones in the literature.
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