In this paper we study the existence and uniqueness of mild and
classical solutions for a nonlinear impulsive integral evolution
equation
$u'(t)= Au(t)+f(t,u(t),\int_0^tk(t,s)u(s)ds),
t>0, t\ne t_i,$
$u(0)= u_0,$
$\Delta u(t_i)=
I_i(u(t_i)). i= 1,2,....,p.$
in a Banach space X, where A is the infinitesimal generator of a
strongly continuous semigroup,$ \Delta u(t_i)=u(t^+_i)-u(t^-_i)$
and $I's$ are some operator. We apply the semigroup theory to study
the existence and uniqueness of the mild solutions, and then show
that the mild solution give rise to classical solution if $f$ is
continuously differentiable.
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