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September  2016, 36(9): 4925-4943. doi: 10.3934/dcds.2016013

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

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

Received  August 2015 Revised  February 2016 Published  May 2016

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.
Citation: Weigao Ge, Li Zhang. Multiple periodic solutions of delay differential systems with $2k-1$ lags via variational approach. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 4925-4943. doi: 10.3934/dcds.2016013
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