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INFINITE DIMENSIONALITY OF THE SOLUTION SPACE OF $y^\prime=0$ ON NON-ARCHIMEDEAN FIELDS }

K. Shamseddine

Abstract


The solution of the simplest differential equation $y^\prime=0$ onnon-Archimedean fields is investigated. Contrary to the real case where theonly solution is the constant function, we show that in the non-Archimedeancase, the solutionspace of the differential equation $y^\prime=0$ is infinite dimensional.This is a unique property of non-Archimedean fields and is connected to theexistence of nontrivial order preserving field automorphisms on such fields,contrary to the real case where the only order preserving fieldautomorphism is the identity map.

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