Unbounded sequences of cycles in generalautonomous equations with periodic nonlinearities

Alexander M. Krasnoselskii

doi:10.3934/dcdss.2013.6.999

Article Contents

2013, Volume 6, Issue 4: 999-1016. Doi: 10.3934/dcdss.2013.6.999

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Unbounded sequences of cycles in general autonomous equations with periodic nonlinearities

Alexander M. Krasnoselskii^1,2,3,

1.
Institute for Information Transmission Problems, Russian Academy of Sciences
2.
19 Bol.Karetny Lane, Moscow GSP-4, 127994, Russia; National Research University Higher School of Economics
3.
20 Myasnitskaya Street, Moscow 101000

Received: April 2011

Revised: February 2012

Published: August 2013

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Abstract

Autonomous higher order differential equations with scalarnonlinearities, periodic with respect to the main phasevariable under appropriate generic conditions, have an infinitesequence of isolated cycles with amplitudes growing to infinityand periods converging to some specific value $T_{0}$.

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Mathematics Subject Classification: Primary: 34C15, 34C25; Secondary: 93C15.

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