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

2003/05/05 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/0305074

7 pages, LaTeX-2e

openalex publication_date 2003/05/05 · arxiv created 2003/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the Cauchy problem for an operator differential equation of the form y'(z) = Ay(z), where A is a closed linear operator on a Banach space over the completion of an algebraic closure of the field of p-adic numbers, a criterion of correct solvability in the class of locally analytic vector-functions is established. It is shown how the Cauchy-Kovalevskaya theorem for p-adic partial differential equations may be obtained as a particular case from this criterion.

Related

• On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers. II
• Elliptic Pseudo-Differential Equations and Sobolev Spaces over p-adic Fields
• Fundamental solutions of pseudo-differential operators over p-adic\n fields
• A constructive proof of the Cauchy-Kovalevskaya theorem for ordinary differential equations
• Some p-adic differential equations