Instantaneous and Noninstantaneous Impulsive Integrodifferential Equations in Banach Spaces

Abstract

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section.

Approximate Controllability and Ulam Stability for Second-Order Impulsive Integrodifferential Evolution Equations with State-Dependent Delay

“…In fact, one always uses integrodiferential equations to describe a model that has heritable characteristics. As a result, these equations have attracted a lot of attention (see for instance, [17][18][19][20][21][22][23]). In [24], the authors studied some local and global existence and uniqueness results for abstract diferential equations with state-dependent argument.…”

Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

“…In [2], Abbas et al discussed the existence of mild solutions for the following nonlocal problem of impulsive integro-differential equations: In [1], the authors considered the following evolution equation with the initial condition:…”

“…It is important to highlight that our paper delves into the problems examined in [2]. We utilized additional valuable tools, specifically the method of global convergence of successive approximations, to derive our results.…”

Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulsions: Existence and Qualitative Results

“…Hernéndez and O'Regan [1] and Pierri et al [2] began by investigating Cauchy problems for first-order evolution equations with instantaneous and non-instantaneous impulses. The works in [3][4][5][6][7][8][9][10][11] and their references include current results for evolution equations with noninstantaneous impulses. Many authors have examined qualitative properties such as existence, uniqueness, and stability for many integral, differential, and integrodifferential equations, see [12] for more details.…”

“…Motivated by the works [4,19,[22][23][24][25][26], we will investigate the existence and attractivity of mild solutions for non-instantaneous integrodifferential equations via resolvent operators with infinite delay:…”