• Previous Article
    Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles
  • DCDS Home
  • This Issue
  • Next Article
    Regularity criteria for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity in a bounded domain
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
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

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

[1]

Chiun-Chuan Chen, Hung-Yu Chien, Chih-Chiang Huang. A variational approach to three-phase traveling waves for a gradient system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021055

[2]

Jing Li, Gui-Quan Sun, Zhen Jin. Interactions of time delay and spatial diffusion induce the periodic oscillation of the vegetation system. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021127

[3]

Seddigheh Banihashemi, Hossein Jafaria, Afshin Babaei. A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021025

[4]

Zaihong Wang, Jin Li, Tiantian Ma. An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1995-1997. doi: 10.3934/dcdsb.2013.18.1995

[5]

Tomasz Kosmala, Markus Riedle. Variational solutions of stochastic partial differential equations with cylindrical Lévy noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2879-2898. doi: 10.3934/dcdsb.2020209

[6]

Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277

[7]

Yumi Yahagi. Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021099

[8]

Nizami A. Gasilov. Solving a system of linear differential equations with interval coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2739-2747. doi: 10.3934/dcdsb.2020203

[9]

Tian Hou, Yi Wang, Xizhuang Xie. Instability and bifurcation of a cooperative system with periodic coefficients. Electronic Research Archive, , () : -. doi: 10.3934/era.2021026

[10]

Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021023

[11]

Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206

[12]

Maoding Zhen, Binlin Zhang, Xiumei Han. A new approach to get solutions for Kirchhoff-type fractional Schrödinger systems involving critical exponents. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021115

[13]

Mengyao Chen, Qi Li, Shuangjie Peng. Bound states for fractional Schrödinger-Poisson system with critical exponent. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021038

[14]

Kazuhiro Kurata, Yuki Osada. Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021100

[15]

V. Vijayakumar, R. Udhayakumar, K. Kavitha. On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay. Evolution Equations & Control Theory, 2021, 10 (2) : 271-296. doi: 10.3934/eect.2020066

[16]

Ahmad El Hajj, Hassan Ibrahim, Vivian Rizik. $ BV $ solution for a non-linear Hamilton-Jacobi system. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3273-3293. doi: 10.3934/dcds.2020405

[17]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

[18]

Xiaoming Wang. Quasi-periodic solutions for a class of second order differential equations with a nonlinear damping term. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 543-556. doi: 10.3934/dcdss.2017027

[19]

Jinyi Sun, Zunwei Fu, Yue Yin, Minghua Yang. Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3409-3425. doi: 10.3934/dcdsb.2020237

[20]

Demou Luo, Qiru Wang. Dynamic analysis on an almost periodic predator-prey system with impulsive effects and time delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3427-3453. doi: 10.3934/dcdsb.2020238

2019 Impact Factor: 1.338

Metrics

  • PDF downloads (43)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]