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In this paper, we answer a question due to Y. André related to B. Dwork's conjecture on a specialization of the logarithmic growth of solutions of  p -adic linear differential equations. Precisely speaking, we explicitly construct a ∇-module  M  over   $\mathbb {Q}_p[\![X]\!]_0$   of rank 2 such that the left endpoint of the special log-growth Newton polygon of  M  is strictly above the left endpoint of the generic log-growth Newton polygon of  M .

A Note on Logarithmic Growth Newton Polygons of p -Adic Differential Equations