一类非线性延迟积分方程概周期型解的存在性

Existence of positive almost periodic type solutions for some nonlinear delay integral equations

1976年,Cook和Kaplan关于人口传染病问题建立了一个数学模型,即一类延迟积分方程,随后一些类似的模型被建立了起来.首先简要介绍了几个延迟积分方程的概周期型解的研究概况,以及概周期函数、渐近概周期和伪概周期函数的定义,最后利用关于Hilbert投影度量不动点理论,讨论了一类延迟积分方程的正的概周期型解的存在性.

Cook and Kaplan gave a mathematical model for epidemics and population in 1976, that is some delay integral equation. Consequently, some similar models are given. The cases of investigation for these equations are briefly introduced; the definitions of almost periodic function, asymptotically almost periodic function and pseudo almost periodic function are given. Finally, the existence of positive almost periodic type solutions for some nonlinear delay integral equations is discussed by applying fixed points theorem on Hilbert project metric.