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

dc.contributor.areaMathematicsen_US
dc.contributor.authorZanini, Chiaraen_US
dc.contributor.authorZanolin, Fabioen_US
dc.contributor.departmentFunctional Analysis and Applicationsen_US
dc.date.accessioned2006-07-21T11:14:25Zen_US
dc.date.accessioned2011-09-07T20:27:34Z
dc.date.available2006-07-21T11:14:25Zen_US
dc.date.available2011-09-07T20:27:34Z
dc.date.issued2006-07-21T11:14:25Zen_US
dc.description.abstractWe 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.extent250816 bytesen_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationNonlinear Anal. Real World Appl. 9 (2008) 141-153en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/1845en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesSISSA;39/2006/Men_US
dc.relation.ispartofseriesarXiv.org;math.CA/0607042en_US
dc.relation.uri10.1016/j.nonrwa.2006.09.008en_US
dc.titleMultiplicity of periodic solutions for differential equations arising in the study of a nerve fiber modelen_US
dc.typePreprinten_US
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