On subharmonics bifurcation in equations with homogeneous nonlinearities

Alexander Krasnosel'skii; Alexei Pokrovskii

doi:10.3934/dcds.2001.7.747

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2001, Volume 7, Issue 4: 747-762. Doi: 10.3934/dcds.2001.7.747

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On subharmonics bifurcation in equations with homogeneous nonlinearities

Alexander Krasnosel'skii^1, and
Alexei Pokrovskii^2,

1.
Institute for Information Transmission Problems, Russian Academy of Sciences, 19 Bolshoi Karetny Lane, Moscow 101447
2.
Institute for Nonlinear Science, Department of Physics, National University of Ireland, University College, Cork

Received: December 31, 2000

Published: September 2001

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Abstract

The bifurcation of subharmonics for resonant nonautonomous equations of the second order is studied. The set of subharmonics is defined by principal homogeneous parts of the nonlinearities provided these parts are not polynomials. Analogous statements are proved for bifurcations of $p$-periodic orbits of a planar dynamical system. The analysis is based on topological methods and harmonic linearization.

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Mathematics Subject Classification: 34C23, 34C35, 54H25, 34H05.

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