DIFFERENTIAL EQUATIONS OVER THE RING OF FUNCTIONS ON A SET OF HOMOMORPHISMS OF THE DIFFERENTIAL RING TO THE RING OF CONSTANTS

Abstract

Let (K, D) be a differential ring and T be some set of homomorphism t : K → C (C be ring constants) that for x, y є K, x ≠ y, there exists t є T, tx ≠ ty. Denote the ring K′ of the functions j : t → tx (x є K) and let (δφ)(t) = t(Dx). Some properties of the linear differential equation (δφ)(t) = A(t)φ(t) + ψ(t) over the ring K′ are obtained.