Linear differential equation with inhomogeneity in the form of a formal power series over a ring with non-Archimedean valuation

• Date: 2026
• Main Authors: Hefter, S. L., Goncharuk, A. B., Гефтер, С. Л., Гончарук, А. Б.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7287
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.922 Consider the linear nonhomogeneous differential equation of $m$-th order with constant coefficients from the valuation ring $K$ of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution from the ring of formal power series $K[[x]]$ of thi...