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Nontrivial periodic solutions to a type of delayed resonant differential equations
Huafeng Xiao,Yuming Chen,Zhiming Guo
Keywords:periodic solution, delay differential equation, Hamiltonian system, Clark dual
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.