# Existence and Asymptotics of Abstract Functional Differential Equations

## TL;DR

This paper extends the Yosida-approximation method to solve nonlinear abstract functional differential equations with finite and infinite delay, providing regularity, boundedness, and asymptotic behavior results.

## Contribution

It generalizes the integral solution approach and applies the Yosida-approximation to establish existence, regularity, and asymptotic properties of solutions for abstract functional differential equations.

## Key findings

- Established existence of solutions using Yosida-approximation
- Proved regularity and boundedness of solutions
- Derived results on asymptotic almost periodicity

## Abstract

It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral solution will provide regularity results. Moreover, this method applies to derive uniform convergence on the halfline, and therefore general results on boundedness and various types of asymptotic almost periodicity.