This paper studies the existence of affine-periodic solutions which have the form of $x(t+T)=Qx(t)$ with some nonsingular matrix Q. Depending on the structure of Q, they can be periodic, anti-periodic, quasi-periodic or even unbounded. Krasnosel’skii–Perov type existence theorem, asymptotic and homotopy equivalence approaches are given.

中文翻译：

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渐近和同伦对等的仿射周期解

本文研究了仿射周期解的存在，其形式为$ x（t + T）= Qx（t）$以及一些非奇异矩阵Q。根据Q的结构，它们可以是周期的，反周期的，准周期甚至无限的。给出了Krasnosel'skii-Perov型存在性定理，渐近和同伦对等的方法。