Consider a linear inhomogeneous differential equation of the mth order with constant coefficients from the valuation ring K of a non-Archimedean field. We establish sufficient conditions for the uniqueness and existence of the solution of this equation in the ring of formal power series K[[x]]. In addition, we obtain a fundamental solution of this equation such that its convolution with the inhomogeneity is a unique solution of the analyzed equation.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 11, pp. 1463–1477, November, 2022. Ukrainian https://doi.org/10.37863/umzh.v74i11.7287.
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Hefter, S.L., Goncharuk, A.B. Linear Differential Equation with Inhomogeneity in the Form of a Formal Power Series Over a Ring with Non-Archimedean Valuation. Ukr Math J 74, 1668–1685 (2023). https://doi.org/10.1007/s11253-023-02163-0
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DOI: https://doi.org/10.1007/s11253-023-02163-0