Existence results for semilinear differential equations with nonlocal and impulsive conditions

Abstract

In this paper, we study the existence of integral solutions for impulsive evolution equations with nonlocal conditions where the linear part is nondensely defined. Some existence results of integral solutions to such problems are obtained under the conditions in respect of the Hausdorff's measure of noncompactness. Example is provided to illustrate the main result. c 2012 NGA. All rights reserved.

On the new concept of solutions and existence results for impulsive fractional evolution equations

“…As we all known, the nonlocal conditions has a better effect on the solution and is more precise for physical measurements than the classical initial condition alone. For the nonlocal impulsive Cauchy problems, we refer the readers to [9,10,11,17] and the references therein.…”

“…For a wide bibliography and exposition on this object see for instance the monographs of [1,2,3,4] and the papers [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19].…”

A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

“…[22][23][24]. The study of dynamical systems with impulsive effects has been an object of investigations [25][26][27][28]. It has been extensively studied under various conditions on the operator A and the nonlinearity f by several authors [29][30][31].…”

Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation

“…In [8], author has shown the controllability of a system of impulsive semilinear non-autonomous differential equations via Rothe's type fixed-point theorem. For more details and study on such differential equation, we refer to the monographs [9,10] and papers [11][12][13][14][15][16][17][18][19][20] and reference cited therein.…”

“…An impulsive neutral integro-differential equation of Sobolev type with time varying delays has been considered by authors in [27] and the sufficient condition for existence of the mild solution has been provided by using the Monch's fixed point theorem. In [14], authors have studied the existence results for the mild solution of a nonlocal differential equation impulsive conditions. The existence results for mild solutions have been obtained via the techniques of approximate solutions and fixed point theorem.…”