Existence And Multiplicity Of Solution For Delay Differential Equation

The research about the delay diferential equation is significant to both the theoryand the practice. On one hand, works in this field will enrich the theory of delay func-tional diferential equation, on the other hand, they could be the basis for the practice.In this paper, we studied the existence and multiplicity of periodic solution fordelay diferential equation. There are two main parts in our paper:（1） The existence and multiplicity of periodic solution for the following secondorder delay diferential equation system via Hamilton system:（P）where τ>0is the delay and f, g∈C¹（R⁴, R） are assumed to be asymptotically linear.（2） The existence and multiplicity of periodic solution for the following secondorder delay diferential equation via variational method:where τ₁>0, τ₂>0are the delays and h∈C¹（R³, R） are assumed to be asymptoti-cally linear.