Periodic solutions for a class of second order ODEs with a Nagumo cubic type nonlinearity

Chiara Zanini; Fabio Zanolin

doi:10.3934/dcds.2012.32.4045

Article Contents

2012, Volume 32, Issue 11: 4045-4067. Doi: 10.3934/dcds.2012.32.4045

This issue Previous Article Asymptotic behavior of singular solutions for a semilinear parabolic equation Next Article

Periodic solutions for a class of second order ODEs with a Nagumo cubic type nonlinearity

Chiara Zanini^1, and
Fabio Zanolin^2,

1.
Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino
2.
Dipartimento di Matematica e Informaticà, Universita di Udine, via delle Scienze 206, 33100 Udine

Received: August 31, 2011

Revised: October 31, 2011

Published: October 2012

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Abstract

We prove the existence of multiple periodic solutions as well as the presence of complex profiles (for a certain range of the parameters) for the steady-state solutions of a class of reaction-diffusion equations with a FitzHugh-Nagumo cubic type nonlinearity. An application is given to a second order ODE related to a myelinated nerve axon model.

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Mathematics Subject Classification: Primary: 34C25, 37E40; Secondary: 92C20.

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