GLOBAL CONTINUA OF PERIODIC SOLUTIONS TO SOME DIFFERENCE-DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

JIANHONG WU

doi:10.2748/tmj/1178225955

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

GLOBAL CONTINUA OF PERIODIC SOLUTIONS TO SOME DIFFERENCE-DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

JIANHONG WU

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Keywords: Global bifurcation, periodic solution, multiplicity, neutral equation, transmission line, equivariant degree

JOURNAL FREE ACCESS

1993 Volume 45 Issue 1 Pages 67-88

DOI https://doi.org/10.2748/tmj/1178225955

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Abstract

In this paper, we apply a global bifurcation theorem of Alexander-Yorke type to investigate the global continua of periodic solutions of a scalar neutral functional differential equation arising from the study of lossless transmission lines. It will be shown that the considered equation has a slowly oscillating periodic solution and several rapidly oscillating periodic solutions. It will also be demonstrated that this seemingly simple equation raises several unanswered questions.

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