Global Existence for some Integro-Differential Equations with Delay Subject to Non-Local Conditions

Abstract

By making use of the Leray-Schauder fixed point theorem we prove the global existence of solutions to some integro-differential equations with delay subject to non-local conditions, and this problem is considered in an arbitrary Banach space.

Long time behavior for a nonlinear fractional model

“…This improves earlier results by the authors (see [6]). To this end we combine some well-known inequalities with a technique of desingularization due to Medved [17,18], Kirane and Tatar [13,14], Tatar [27] and Mazouzi and Tatar [16].…”

Existence and Osgood Type Uniqueness of Mild Solutions of Nonlinear Integrodifferential Equation With Nonlocal Condition

“…Subsequently some authors have been studied the problems of existence, uniqueness and other properties of solutions of (1.1) or their special forms by using different techniques, see [1,2,3,8,12,14,15] and the references cited therein. We also refer some papers and monographs [11,12,18], [1, p. 342], [6, p.308], [10, p. 18].…”

Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces

“…Subsequently he has investigated the same problem for different types of evolution equations in Banach spaces [7][8][9][10]. Many papers have been appeared on nonlocal Cauchy problem for various classes of differential and integrodifferential equations [13][14][15][16]. Physical motivation for this kind of problem is given in [6][7][8][9][10].…”