Multiple periodic solutions of delay differential systems with $2k-1$ lags via variational approach

Weigao  Ge; Li  Zhang

doi:10.3934/dcds.2016013

Article Contents

2016, Volume 36, Issue 9: 4925-4943. Doi: 10.3934/dcds.2016013

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Multiple periodic solutions of delay differential systems with $2k-1$ lags via variational approach

Weigao Ge^1, and
Li Zhang^2,

1.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081
2.
Department of Foundation Courses, Beijing Union University, Beijing 100101

Received: August 2015

Revised: February 2016

Published: May 2017

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Abstract

By variational methods, this paper considers 4k-periodic solutions of a kind of differential delay systems with $2k-1$ lags. Our results reveal the fact that the number of $4k-$periodic orbits depends only upon the eigenvalues of both matrices $A_{\infty}$ and $A_0$. The conditions are more definite and easier to be examined. Moreover, two examples are given to illustrate the applications of the results.

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Mathematics Subject Classification: Primary: 34K13; Secondary: 58E50.

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