# American Institute of Mathematical Sciences

November  2012, 32(11): 4045-4067. doi: 10.3934/dcds.2012.32.4045

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

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

Received  September 2011 Revised  November 2011 Published  June 2012

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.
Citation: Chiara Zanini, Fabio Zanolin. Periodic solutions for a class of second order ODEs with a Nagumo cubic type nonlinearity. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 4045-4067. doi: 10.3934/dcds.2012.32.4045
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