Abstract
Proc. Japan Acad. Ser. A Math. Sci. Volume 87, Number 3 (2011),
40-43 Let $\mathcal{M}$ be a differential module, whose coefficients are analytic
elements on an open annulus $I$ ($\subset \bR_{>0}$) in a valued field,
complete and algebraically closed of inequal characteristic, and let
$R(\mathcal{M}, r)$ be the radius of convergence of its solutions in the
neighbourhood of the generic point $t_r$ of absolute value $r$, with $r\in I$.
Assume that $R(\mathcal{M}, r)<r$ on $I$ and, in the logarithmic coordinates,
the function $r\longrightarrow R(\ mathcal{M}, r)$ has only one slope on $I$.
In this paper, we prove that for any $r\in I$, all the solutions of
$\mathcal{M}$ in the neighborhood of $t_r$ are analytic and bounded in the disk
$D(t_r,R(\mathcal{M},r)^-)$.