NONTRIVIAL PERIODIC SOLUTIONS TO A TYPE OF DELAYED RESONANT DIFFERENTIAL EQUATIONS

Huafeng Xiao; Yuming Chen; Zhiming Guo

doi:10.11948/20190024

2019 Volume 9 Issue 6

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Huafeng Xiao, Yuming Chen, Zhiming Guo. NONTRIVIAL PERIODIC SOLUTIONS TO A TYPE OF DELAYED RESONANT DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2245-2260. doi: 10.11948/20190024

Citation:

Huafeng Xiao, Yuming Chen, Zhiming Guo. NONTRIVIAL PERIODIC SOLUTIONS TO A TYPE OF DELAYED RESONANT DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2245-2260. doi: 10.11948/20190024

NONTRIVIAL PERIODIC SOLUTIONS TO A TYPE OF DELAYED RESONANT DIFFERENTIAL EQUATIONS

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, China
2.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Corresponding author: Email address:guozm@gzhu.edu.cn(Z. Guo)
Fund Project: The authors were supported by National Natural Science Foundation of China (NO. 11771104, 11871171) and Innovative Research Team in University (IRT_16R16)

Abstract

Abstract

In this paper, we consider a type of delayed resonant differential equations. We focus on the existence of periodic solutions. Employing the Clark dual, we provide two sets of criteria on the existence of at least one periodic solution. In fact, the periodic solutions are critical points minimizing the dual functional of the coupled Hamiltonian system on certain subspaces of a Banach space.
- Periodic solution /
- delay differential equation /
- Hamiltonian system /
- Clark dual
MSC: 34K13

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References

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