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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,

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.
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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show all references

References:
[1]

Discrete and Cont. Dynamicals Sys., 3 (1997), 251-264. doi: 10.3934/dcds.1997.3.251.  Google Scholar

[2]

Nonlinear Anal., 65 (2006), 25-39. doi: 10.1016/j.na.2005.06.011.  Google Scholar

[3]

Nonlinear Anal., 65 (2006), 40-58. doi: 10.1016/j.na.2005.06.012.  Google Scholar

[4]

Acta Appl. Math. Sinica(in Chinese), 17 (1994), 173-181. Google Scholar

[5]

Chinese Sci. Bull., 42 (1997), 444-447. doi: 10.1007/BF02882587.  Google Scholar

[6]

Acta Math. Sinica(New Series), 12 (1996), 113-121. doi: 10.1007/BF02108151.  Google Scholar

[7]

Chinese Ann. Math., 15 (1994), 217-224.  Google Scholar

[8]

J. Differential Equations, 218 (2005), 15-35. doi: 10.1016/j.jde.2005.08.007.  Google Scholar

[9]

J. Dynam. Differential Equations, 23 (2011), 1029-1052. doi: 10.1007/s10884-011-9228-z.  Google Scholar

[10]

J. Math. Anal. Appl., 48 (1974), 317-324. doi: 10.1016/0022-247X(74)90162-0.  Google Scholar

[11]

Nonlinear Anal., 31 (1998), 45-54. doi: 10.1016/S0362-546X(96)00058-2.  Google Scholar

[12]

Sci. China Ser. A, 42 (1999), 957-964. doi: 10.1007/BF02880387.  Google Scholar

[13]

Nonlinear Analysis, TMA, 35 (1999), 457-474. doi: 10.1016/S0362-546X(97)00623-8.  Google Scholar

[14]

J. Differential Equations, 78 (1989), 53-73. doi: 10.1016/0022-0396(89)90075-2.  Google Scholar

[15]

Springer-Verlag, New Yorke, 1989. doi: 10.1007/978-1-4757-2061-7.  Google Scholar

[16]

Proc. Loyal Soc. Edingburgh, 81 (1978), 131-151. doi: 10.1017/S0308210500010490.  Google Scholar

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