  We consider a vector bundle with integrable connection (\cE,\na) on an
analytic domain U in the generic fiber \cX_{\eta} of a smooth formal p-adic
scheme \cX, in the sense of Berkovich. We define the \emph{diameter}
\delta_{\cX}(\xi,U) of U at \xi\in U, the \emph{radius} \rho_{\cX}(\xi) of the
point \xi\in\cX_{\eta}, the \emph{radius of convergence} of solutions of
(\cE,\na) at \xi, R(\xi) = R_{\cX}(\xi, U,(\cE, \na)). We discuss (semi-)
continuity of these functions with respect to the Berkovich topology. In
particular, under we prove under certain assumptions that \delta_{\cX}(\xi,U),
\rho_{\cX}(\xi) and R_{\xi}(U,\cE,\na) are upper semicontinuous functions of
\xi; for Laurent domains in the affine space, \delta_{\cX}(-,U) is continuous.
In the classical case of an affinoid domain U of the analytic affine line, R is
a continuous function.
