一阶泛函差分方程正周期解的存在性

Existence of Positive Periodic Solutions for the First-Order Delayed Difference Equations

考虑了一阶泛函差分方程△x(n)=a(n)g(x(n))x(n)-λb(n)f(x(n-r(n))),n∈Z正周期解的存在性.其中f,g∈C([0,∞),[0,∞)),λ为参数数运用不动点指数理论获得了上述问题正周期的存在性结果,所得结果推广了Raffoul的相关结果.

We are concerned with the existence of positive periodic solutions for the first-order delayed difference equations Δ x（n）=a（n）g（x（n））x（n）-λb（n）f（x（n-τ（n）））,n∈Z where f,g∈C（[0,∞）,[0,∞））, λ is a parameter. By using the fixed-point index theory, we establish the existence results of positive periodic solutions for the above problem. Our results generalize some results by Raffoul.