Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation

Abstract

In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.

On efficient abstract method for the study of Cauchy problem for a second order differential equation set on a singular cylindrical domain

“…Then, we have opted for the use of another approach based essentially on the theory of abstract differential equations. The effectiveness of this method was manifested in several works, see for example [2], [3], [5], [7], [8], [18] and the references cited therein. Our purpose is to establish existence, uniqueness and maximal regularity of the strict solution for (1.2)-(1.3).…”

CONTROLLABILITY OF SOBOLEV TYPE NONLOCAL IMPULSIVE MIXED FUNCTIONAL INTEGRODIFFERENTIAL EVOLUTION SYSTEMS Vol. 3(1) Jan 2015, No. 11, pp. 122-132 KAMALENDRA KUMAR, RAKESH KUMAR

“…On the other hand, most of the practical systems are integrodifferential equations in nature and hence the study of integrodifferential equations is very important. Many authors studied mixed type integrodifferential systems with (or without) delay conditions [11], [23], [24], [28], [29], and [30]. Recently, Machado et al [22] establish the controllability for a class of abstract impulsive mixed type functional integrodifferential equations with finite delay in a Banach space by using the Mö nch fixed point theorem via measure of noncompactness and semigroup theory.…”

Sobolev-Type Volterra-Fredholm Functional Integrodifferential Equations in Banach Spaces

“…Many authors have studied the existence, uniqueness, continuation and other properties of solutions of various special forms of the equations (1.1)-(1.2) and (1.3)-(1.4) by using different techniques, see for example, [7]- [11], [16]- [18], [21] and some of the references given therein.…”