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 $D(t_r,R(\mathcal{ M},r)^-)$.
Categories: math.NT