Existence of Mild and Classical Solutions for Nonlocal Impulsive Integrodifferential Equations in Banach Spaces with Measure of Noncompactness

K Karthikeyan,K Malar,A Anguraj,Juan J Trujillo

doi:10.1155/2014/319250

Abstract

We study the existence of mild and classical solutions are proved for a class of impulsive integrodifferential equations with nonlocal conditions in Banach spaces. The main results are obtained by using measure of noncompactness and semigroup theory. An example is presented.

Highlights

We are concerned with the existence of mild and classical solutions are proved for a class of impulsive integrodifferential equations with nonlocal conditions: u󸀠 (t) = Au (t)
The theory of semigroups of bounded linear operators is closely related to the solution of differential and integrodifferential equations in Banach spaces
Lizama and Pozo [8] investigated the existence of mild solutions for semilinear integrodifferential equation with nonlocal initial conditions by using Hausdorff measure of noncompactness via a fixed point

Summary

Introduction

We are concerned with the existence of mild and classical solutions are proved for a class of impulsive integrodifferential equations with nonlocal conditions: u󸀠 (t) = Au (t). In [7], Xue studied the semilinear nonlocal differential equations with measure of noncompactness in Banach spaces. Lizama and Pozo [8] investigated the existence of mild solutions for semilinear integrodifferential equation with nonlocal initial conditions by using Hausdorff measure of noncompactness via a fixed point. In [24], the authors studied the existence of mild solutions to an impulsive differential equation with nonlocal conditions by applying DarboSadovskii’s fixed point theorem. In recent paper [25], Ahmad et al studied nonlocal problems of impulsive integrodifferential equations with measure of noncompactness.

Preliminaries

Classical Solutions

Example