Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation

2021/12/05 by S. L. Gefter, Sergey Gefter, Gefter, Sergey +3
Mathematics · #12J25 #13B25 #13F25 #34A30 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical and Theoretical Analysis #advanced mathematical theories #math.AC #math.CA #msc:12J25 #msc:13B25 #msc:13F25 #msc:34A30

paper · pdf · doi:10.48550/arxiv.2112.02528

17 pages

arxiv created 2021/12/05 · openalex publication_date 2021/12/05 · arxiv updated 2021/12/07 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28

Abstract

Consider the linear 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 of this equation from K[[x]]. Also the fundamental solution from (1)/(x)K[[(1)/(x)]] 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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