依赖时变无穷时滞的抽象泛函微分方程的演化族与常数变易公式
Evolution families and variation of constants formula for abstract functional differential equations with time-dependent infinite delay
AI总结：
针对含时变无穷时滞的一阶抽象泛函微分方程，本文建立了其温和解的存在性，证明了对应线性方程的解映射族构成演化族，并推导了非齐次线性问题的常数变易公式。
AI中文摘要：
本文在巴拿赫空间中考虑一类一阶抽象时滞泛函微分方程，其包含由正则函数控制的时变无穷时滞。我们建立了该非线性方程温和解的存在性，证明了线性方程的解映射族在适当相空间上构成良定的有界线性算子演化族，进一步利用该演化族证明了非齐次线性问题的常数变易公式。
英文摘要：
In this paper, we consider a class of first-order abstract retarded functional differential equations in Banach spaces, incorporating a time-dependent infinite delay governed by a regulated function. We establish the existence of mild solutions for the nonlinear equation and show that the family of solution maps for the linear equation forms a well-defined evolution family of bounded linear operators on an appropriate phase space. Furthermore, we leverage this evolution family to prove a variation of constants formula for the inhomogeneous linear problem.
