On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers. II

2003/12/01 by Myroslav L. Gorbachuk, Gorbachuk, Myroslav L., Valentyna I. Gorbachuk +2
Mathematics · #12H25 #34G10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.AP #math.NT #msc:12H25 #msc:34G10

paper · pdf · doi:10.48550/arxiv.math/0312026

9 pages, LaTeX-2e

arxiv created 2003/12/01 · openalex publication_date 2003/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an operator-differential equation of the form y^(m)(z) = Ay(z), where A is a closed linear operator on a Banach space over the the field of p-adic numbers, the necessary and sufficient conditions on initial data for the Cauchy problem to be well-posed in the class of locally analytic vector-valued functions are given. The result is illustrated by p-adic partial differential equations.

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