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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
Weigao Ge 1, and Li Zhang 2,
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
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.
Keywords: Periodic solution, critical point., variational approach, differential delay system.
Mathematics Subject Classification: Primary: 34K13; Secondary: 58E5.
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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Weigao Ge Li Zhang