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A general method for the existence of periodic solutions of differential systems in the plane

TitleA general method for the existence of periodic solutions of differential systems in the plane
Publication TypeJournal Article
Year of Publication2012
AuthorsFonda, A, Sfecci, A
JournalJournal of Differential Equations
Volume252
Pagination1369 - 1391
ISSN0022-0396
KeywordsNonlinear dynamics; Periodic solutions
Abstract

We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

URLhttp://www.sciencedirect.com/science/article/pii/S0022039611003196
DOI10.1016/j.jde.2011.08.005

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