# Whole Line Solutions to Abstract Functional Differential Equations

## TL;DR

This paper extends the linear Yosida-approximation method to solve nonlinear and multivalued functional differential equations, analyzing solution properties like boundedness and periodicity in both finite and infinite delay cases.

## Contribution

It introduces a novel application of the Yosida-approximation to a broad class of functional differential equations, including nonlinear and multivalued cases.

## Key findings

- Solution boundedness depends on delay type
- Periodic and almost periodic solutions characterized
- Method applicable to nonlinear, multivalued equations

## Abstract

In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in& A(t,u_t)u(t) +\omega u(t), \ t \in \mathbb{R} \end{eqnarray*} Furthermore, in the case of finite and infinite delay we give an answer about whether the solution is bounded, periodic, almost periodic, or some kind of almost automorphy.