A class of integrodifferential equations and applications (Q934427)

The author considers the integro-differential equation \[ u'(t)=A(\varepsilon)u(t)+\int_0^tF(t-s)u(s)\,ds+Ku(t)+f(t),\;t\geq 0,\quad u(0)=u_0,\tag{1} \] where \(\varepsilon\) is a multi-parameter, \(A(\varepsilon)\) is a linear closed operator in a Banach space \(X\), and \(K\) and \(F(t)\) are bounded operators on \(X\). By using integrated semigroup theory, the continuous dependence of the solution of (1) on \(\varepsilon\) is studied.