发表机构
Università Politecnica delle Marche; Università della Calabria; Università di Messina（马尔凯理工大学; 卡拉布里亚大学; 墨西拿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究乘积空间中仿射变换下的伯克霍夫-凯洛格定理，给出参数依赖解存在准则，通过二阶泛函微分方程组实例说明理论结果，并提供具体例子及数值解、相关常数计算，展现理论应用。
AI 中文摘要
我们证明了仿射变换下乘积空间中的伯克霍夫-凯洛格定理版本。这是处理参数依赖的泛函微分方程组时出现的自然框架。我们给出了所有分量非平凡的参数依赖解存在的准则。在二阶泛函微分方程组情形中说明了理论结果，其泛函部分可涵盖依赖时间和状态的偏差变元的有趣情形。我们提供了一个具体例子，给出了数值近似解，与理论框架一致，并计算或估计了抽象结果所需的所有常数。
英文摘要
We prove a version of the Birkhoff-Kellogg theorem in product spaces, under affine transformations. This is a fairly natural framework that arises when dealing with parameter-dependent systems of functional-differential equations. We provide criteria on the existence of parameter-dependent solutions that have all the components nontrivial. The theoretical results are illustrated in the case of systems of second order functional-differential equations, where the functional part can cover the interesting cases of time and state-dependent deviated arguments. We provide a concrete example, for which we furnish numerically approximated solutions, coherent with our theoretical framework, and in which we compute or estimate all the constants that are required by our abstract results.
Comments22 pages, 6 figures
