Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model

dc.creatorZanini, Chiara
dc.creatorZanolin, Fabio
dc.date2006-07-03
dc.date.accessioned2026-07-07T07:17:55Z
dc.date.available2026-07-07T07:17:55Z
dc.descriptionWe deal with the periodic boundary value problem for a second-order nonlinear ODE which includes the case of the Nagumo type equation $v_{xx} - g v + n(x) F(v) = 0,$ previously considered by Grindrod and Sleeman and by Chen and Bell in the study of the model of a nerve fiber with excitable spines. In a recent work we proved a result of nonexistence of nontrivial solutions as well as a result of existence of two positive solutions, the different situations depending by a threshold parameter related to the integral of the weight function $n(x).$ Here we show that the number of positive periodic solutions may be very large for some special choices of a (large) weight $n.$ We also obtain the existence of subharmonic solutions of any order. The proofs are based on the Poincaré - Bikhoff fixed point theorem.
dc.description18 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0607042
dc.identifierhttp://arxiv.org/abs/math/0607042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114118
dc.subjectClassical Analysis and ODEs
dc.subject34C25; 37E40; 92C20
dc.titleMultiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model
dc.typetext

Files

Collections