Existence Results for Partial Neutral Functional Differential Equations with Unbounded Delay

Abstract

This work is concerned with a class of quasi-linear partial neutral functional differential equations with unbounded delay. Specifically, we establish existence of mild and strong solutions for equations that can be described as an abstractis the infinitesimal generator of a strongly continuous semigroup of linear operators on a Banach space and F and G are appropriate functions defined on a phase space. ᮊ

Controllability of Second-Order Impulsive Functional Differential Equations With State-Dependent Delay

“…The reader is referred to [1,4,5,7,8,[11][12][13][14]32] and references therein for some examples and applications. The problem of the existence of solutions of functional differential equations with state-dependent delay has been treated recently in [2,[16][17][18][19][20]25]. The literature related to second order nonlinear systems with state-dependent delay is not vast, to our knowledge, in the recent works [6,15].…”

Controllability of Damped Second-Order Neutral Impulsive Stochastic Functional Differential Systems with Infinite Delay

“…The book [6] contains the fundamental theory related to functional differential equations with infinite delay. Several works have been established in this direction, we refer to [7,8,9,10,11,12].…”

Regularity for Fractional Order Retarded Neutral Differential Equations in Hilbert Spaces

“…In [4,7,8], the authors have discussed the existence of solutions for mild solutions for the neutral differential systems with state-dependence delay. Most studies about the neutral initial value problems governed by retarded semilinear parabolic equation have been devoted to the control problems.…”