Leslie-Gower或Holling-Tanner型周期捕食系统的正周期解
Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type
摘要：
本文考虑Leslie-Gower型或Holling-Tanner型周期捕食系统，假定系数为连续正$ω$ -周期函数.在带锥的巴拿赫空间中，利用算子方法证明了正$ω$ -周期解的存在性.除了正性和周期性外，系数不需要构造性条件。最后指出，所用的方法可以应用于证明正的$ω$ -周期解的存在性，即使在一定的延迟的情况下，轻微的变化。
英文摘要：
In this paper, we consider periodic predator-prey systems of Leslie-Gower or Holling-Tanner type, assuming that the coefficients are continuous positive $ω$-periodic functions. We prove an existence of positive $ω$-periodic solutions by means of operator method in Banach spaces with cones. No constructive conditions are required for the coefficients, besides the positivity and periodicity. At the end we point out that the used approach can be applied with minor changes for proving the existence of positive $ω$-periodic solutions even in the case of certain delays.
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