Existence results for partial neutral functional integrodifferential equations with unbounded delay

Abstract

We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray-Schauder alternative.  2004 Elsevier Inc. All rights reserved.

Existence and Stability of Solutions for Bilinear Control System with Rieman-Leovel Initial Condition

“…Sobolev type differential Equations have been investigated by many authors, as examples, [1] and [2]. They established the existence of solutions of nonlinear impulsive fractional integro-differential Equations of sobolev type with nonlocal condition.…”

Existence Results for Abstract Degenerate Neutral Functional Differential Equations

“…In the papers [16][17][18] the system (1.3)-(1.4) was studied assuming that A is the generator of an analytic semigroup (T (t)) t≥0 and under a more general and less restrictive assumption on g(·), which is a particular case of the following condition.…”

“…In these it is assumed that A is the generator of a compact C 0 -semigroup (T (t)) t≥0 and the set {AT (t) : t ∈ (0, b]} is bounded in the operator topology. However, as has been pointed out in [16], these conditions are valid if and only if A is bounded and dim X < ∞, which restricts the applications to ordinary differential equations. Moreover, if the compactness assumption is removed, it follows that A is bounded, which remains a strong restriction.…”

Existence results for abstract neutral functional differential equations

“…In these works, is the generator of a 0 -semigroup, and it is assumed that the set { ( ) : ∈ (0, ]}, ( > 0), is bounded in the operator topology. However, as was pointed out in [18], this condition is valid if and only if is a bounded, which restricts the applications to ordinary neutral differential equations.…”