Integrodifferential equations of Volterra type with nonlocal and impulsive conditions

Abstract

This work is devoted to the study of a class of nonlocal impulsive integrodifferential equations of Volterra type. We investigate the situation when the resolvent operator corresponding to the linear part of {dxdt(t)=A(t)x(t)+∫0tΓ(t,s)x(s)ds+f(t,x(t)),t∈I=[0,T],t≠ti,i=1,2,3,…⁡,m,x(ti+)=x(ti)+Ji(x(ti)),x(0)=x0+g(x), is norm continuous. Our results are obtained by using the Hausdorff measure of noncompactness and fixed point theorems. An example is provided to illustrate the basic theory of this work.

Topics & Concepts