本文利用$k-$集压缩算子的拓朴度抽象连续定理和某些分析技巧,研究了一 类中立型对数种群模型 $$\frac{\mathrm{d}N}{\mathrm{d}t}=N(t)[r(t)-a(t)\ln N(t-\sigma )-b(t)\frac{\mathrm{d}}{\mathrm{d}t}\ln N(t-\tau )]$$ 的正周期解存在性问题.得到了正周期解存在性的新结果.

In this paper, the authors employ an abstract continuous theorem of k-set contractive operator and some analysis techniques to study the existence of positive periodic solutions for a neutral delay logarithmic population model as follows. $$\frac{\mathrm{d}N}{\mathrm{d}t}=N(t)[r(t)-a(t)\ln N(t-\sigma )-b(t)\frac{\mathrm{d}}{\mathrm{d}t}\ln N(t-\tau )].$$ A new result on the existence of positive periodic solutions is obtained.