Existence results for an impulsive neutral integro-differential equations in Banach spaces

Abstract

In this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

Characteristics of solutions of nonlinear neutral integro-differential equation via Chandrasekhar integral

“…This is largely due to the fact that often the qualitative behavior of solutions of neutral differential equations is very different from those of nonneutral equations. For example, [10,15,16,19]. It has been shown in the literature that even when all the characteristic roots of a neutral differential equation have negative real parts, it is still possible for the equation to have unbounded solutions.…”