Abstract
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.
Original language | English (US) |
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Pages (from-to) | 245-252 |
Number of pages | 8 |
Journal | Transactions of the American Mathematical Society |
Volume | 271 |
Issue number | 1 |
DOIs | |
State | Published - May 1982 |