Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model
dc.contributor.area | Mathematics | en_US |
dc.contributor.author | Zanini, Chiara | en_US |
dc.contributor.author | Zanolin, Fabio | en_US |
dc.contributor.department | Functional Analysis and Applications | en_US |
dc.date.accessioned | 2006-07-21T11:14:25Z | en_US |
dc.date.accessioned | 2011-09-07T20:27:34Z | |
dc.date.available | 2006-07-21T11:14:25Z | en_US |
dc.date.available | 2011-09-07T20:27:34Z | |
dc.date.issued | 2006-07-21T11:14:25Z | en_US |
dc.description.abstract | 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 Poincar\'{e} - Bikhoff fixed point theorem. | en_US |
dc.format.extent | 250816 bytes | en_US |
dc.format.mimetype | application/pdf | en_US |
dc.identifier.citation | Nonlinear Anal. Real World Appl. 9 (2008) 141-153 | en_US |
dc.identifier.uri | https://openscience.sissa.it/handle/1963/1845 | en_US |
dc.language.iso | en_US | en_US |
dc.relation.ispartofseries | SISSA;39/2006/M | en_US |
dc.relation.ispartofseries | arXiv.org;math.CA/0607042 | en_US |
dc.relation.uri | 10.1016/j.nonrwa.2006.09.008 | en_US |
dc.title | Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model | en_US |
dc.type | Preprint | en_US |