Generalized Cauchy problems involving nonlocal and impulsive conditions

Abstract

We study the abstract Cauchy problem involving a class of nonlinear differential inclusions, with impulsive and nonlocal conditions. By using MNC estimates, the existence result and continuous dependence on initial data of the solution set are proved.

Existence results for fractional integro-differential inclusions with state-dependent delay

“…For this reason, we next recall a few properties of this concept. For general information the reader can see [5,6,9,25,28]. In this work, we use the notion of Hausdor measure of noncompactness.…”

Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

“…For this reason this topic has attracted the attention of many authors in the last time. We only mention here the papers [7][8][9][10][11][12][13][14][15][16][17] which are directly related with the objective of this paper.…”

“…On the other hand, it is well known that retarded functional differential equations are used to model important concrete phenomena. For general aspects of the theory of partial differential equations with delay we refer to [27], and for functional differential inclusions we refer to [7,9,[12][13][14]28]. In similar way, there exists an extensive literature concerning abstract second order problems.…”

“…In Section 3 we discuss the existence of mild solutions to problems (1)- (4). Finally, in Section 4 we apply our results to establish the existence of solutions to problems (5)- (9).…”

Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces

“…Then an increasing interest has arisen in various nonlocal problems for differential equations and inclusions. Without stressing to wide list of references, we quote here some remarkable solvability results in [9,15,20,21,32]. On the other hand, impulsive conditions has been used to describe the dynamical systems having abrupt changes.…”