Abstract:The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has an algebraically closed field of constants. In this paper, we prove the existence of a Picard-Vessiot extension for a homogeneous linear differential equation defined over a real differential field K with real closed field of constants. We give an adequate definition of the differential Galois group of a Picard-Vessiot extension of a … Show more
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