A note on non-Robba p-adic differential equations

Let M be a differential module; whose coefficients are analytic elements on an open annulus I (subset of R->0) in a valued field; complete and algebraically closed of inequal characteristic, and let R(M, r) be the radius of convergence of its solutions in the neighborhood of the generic point t(gamma) of absolute value gamma, with gamma is an element of I. Assume that R(M, gamma) < gamma on I and, in the logarithmic coordinates, the function gamma -> R(M, gamma) has only one slope on I. In this paper, we prove that for any gamma is an element of I, all the solutions of M in the neighborhood of t(gamma) are analytic and bounded in the disk D(t(gamma), R(M, gamma)(-)).