| Abstract: |
| In 1934, Volterra poineered the use of an integro-differential equation to model the laboratory populations of some species of small organisms with short generation time. Since then, numerous differential equations incorporating distributed delay have been constructed. Utilizing tools such as fixed point theory, the existence of periodic solutions for these rypes of equations has been established. Recently, Nakata investigated a differential eqution with distributed delay, establishing the existence of at least one periodic solution. However, subsequent numerical simulations have intriguingly revealed the presence of the existence of two periodic solutions. Recognizing the significance of this discovery, our report delves into the matter further, exploring the multiplicity of periodic solutions in differential equations with distributed delay. We achieve this by making use of the critical point theory, equivariant degree theory and Kaplan-Yorke`s method. This is jointed work with Prof. Zhiming Guo, Wieslaw Krawcewicz, Jianshe Yu, et. al. |
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