Growth of solutions of linear differential equations at a logarithmic singularity

We consider differential equations Y' = AY with a regular singular point at the origin, where A is an n X n matrix whose entries are p-adic meromorphic functions. If the solution matrix at the origin is of the form Y — P exp(θ log x), where P is an n X n matrix of meromorphic functions and θ is an n X n constant matrix whose Jordan normal form consists of a single block, then we prove that the entries of P have logarithmic growth of order n — 1.