Linear differential equation with inhomogeneity in the form of a formal power series over a ring with non-Archimedean valuation
Abstract
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 this equation. Also the fundamental solution of the equation is obtained and it is shown that the convolution of the fundamental solution and a non-homogeneity is a unique solution of the equation.
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