Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model
| dc.creator | Zanini, Chiara | |
| dc.creator | Zanolin, Fabio | |
| dc.date | 2006-07-03 | |
| dc.date.accessioned | 2026-07-07T07:17:55Z | |
| dc.date.available | 2026-07-07T07:17:55Z | |
| dc.description | We 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.description | 18 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0607042 | |
| dc.identifier | http://arxiv.org/abs/math/0607042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114118 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34C25; 37E40; 92C20 | |
| dc.title | Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model | |
| dc.type | text |