Existence Theorem for Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions

Abstract

The existence, uniqueness and continuous dependence of a mild solution of a Cauchy problem for semilinear impulsive first and second orderfunctional differential-equations with nonlocal conditions in general Banach spaces are studied. Methods of fixed point theorems, of a C0 semigroup of operators and the Banach contraction theorem are applied

Existence of mild solutions of second-order impulsive differential equations in Banach spaces

“…The authors [6] considered the existence of mild solutions for a class of abstract impulsive second-order neutral functional differential equations. In [10], the authors studied the abstract second-order nonlinear impulsive differential equation with nonlocal condition…”

About the Nature of the Spectrum of the Periodic Problem for the Heat Equation with a Deviating Argument

“…The equation that we studied belongs to a class of functional-differential equations. These equations have only recently become a subject of research of individual authors; particularly, such equations are studied in [4][5][6]. Functionaldifferential equations have been actively studied recently by some authors in papers [7,8].…”