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Zbl 0905.34038
Manásevich, Raúl; Mawhin, Jean
Periodic solutions for some nonlinear systems with $p$-Laplacian like operators. (English)
[A] García, C. (ed.) et al., Proceedings of the 4th Catalan days on Applied Mathematics, Tarragona, Spain, February 11-13, 1998. Tarragona: Univ., Department d'Enginyeria Informàtica, 103-122 (1998).

The existence of a periodic solution is reduced by the Poincaré method of sections to the existence of a fixed point. The period $T$ of the periodic solution (`distance' between sections) is presumed to be known. It is not specified whether the `forcing function' $f$ is periodic or not. It is not known in advance whether nonresonant, resonant harmonic, resonant subharmonic, or autonomous periodic solutions are considered.\par The method of reduction is not constructive, merely `very' general. No indication is given whether all imposed conditions are necessary.
[I.Gumowski (Thoiry)]

MSC 2000:: *34C25 Periodic solutions of ODE
34B15 Nonlinear boundary value problems of ODE

Keywords: nonconstructive conditions; existence; Poincaré method of sections

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