| Contents |
| We consider the Cauchy problem
\begin{eqnarray}\label{te0}
u'=Au+\int_{0}^{t}g(t-s,u(s))ds+f(t,u(t)),\ t>0,\\
u(0)=u_0\in X_1=D(A),\label{ic0}
\end{eqnarray}
where $A:D(A)\subset X_0\longrightarrow X_0$ is a linear operator such that $-A$ is a sectorial operator, $X_0$ is a Banach space, and $g$ and $f$ are functions mapping $X_1$ into $X_\alpha$, satisfying certain conditions. We purpose to present a result on existence and uniqueness of mild solutions for the above problem, when $\alpha\in(0,1]$. |
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