On existence and continuation of mild solutions of functional-differential equations of neutral type in Banach spaces

TL;DR

This paper investigates conditions under which mild solutions of neutral type functional-differential equations in Banach spaces exist and can be extended to the domain boundary, using fixed point theory.

Contribution

It establishes new criteria for existence and continuation of solutions in Banach spaces employing Schauder fixed point theorem.

Findings

Proved existence of mild solutions under specific conditions.

Established criteria for continuation of solutions to the boundary.

Applied Schauder fixed point theorem to functional-differential equations.

Abstract

The aim of this work is to investigate the conditions for the existence and continuation of a mild solution to the initial value problem of functional-differential equations of neutral type in Banach spaces to the boundary of the domain. Based on the Schauder fixed point theorem, the existence and continuation to the boundary of the domain are proved.