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- W2897733703 abstract "We consider the problem of the existence and multiplicity of periodic solutions associated to a class of scalar equations of the form x ″ + f ( t , x ) = 0 . The class considered is such that the behaviour of its solutions near zero and infinity can be compared two suitable piecewise linear systems. We show how a rotation number approach, together with the Poincaré–Birkhoff theorem and the phase-plane analysis of the spiral properties, allows to obtain multiplicity results in terms of the gap between the rotation numbers of the referred piecewise linear systems at zero and at infinity. These systems may also be resonant. In particular, our approach can be used to deal with the problems without both global existence of the Cauchy problems associated to the equation and the sign assumption on f . The typical example is a partially superlinear second order equation. Our main result generalizes some classical results of Jacobowitz and Hartman, among others." @default.
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- W2897733703 date "2019-04-01" @default.
- W2897733703 modified "2023-10-16" @default.
- W2897733703 title "Periodic solutions of second order equations via rotation numbers" @default.
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- W2897733703 doi "https://doi.org/10.1016/j.jde.2018.10.010" @default.
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