神经纤维模型中微分方程周期解的多重性
Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model
摘要：
我们讨论了二阶非线性常微分方程的周期边值问题，其中包括Grindrod和Sleeman以及Chen和Bell在研究具有可兴奋棘的神经纤维模型时考虑的Nagumo型方程$v_{xx} - g v + n(x) F(v) = 0,$的情况。在最近的工作中，我们证明了非平凡解的不存在性以及两个正解的存在性的结果，不同的情况取决于与权函数$n(x).$的积分有关的门限参数。在这里，我们证明了对于a（大）的某些特殊选择，正周期解的数目可能非常大。权$n.$我们还得到了任意阶的下调和解的存在性.证明基于Poincaré - Bikhoff不动点定理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
