Pseudo-Differential Equations with Weak Degeneration for Radial Functions of $p$-adic Argument
Classical Analysis and ODEs
2023-01-24 v2 Number Theory
Abstract
In earlier papers (A. N. Kochubei, Pacif. J. Math., 269 (2014), 355-369; J. Math. Anal. Appl.483 (2020), Article 123609), one of the authors developed a theory of pseudo-differential equations for radial real-valued functions on a non-Archimedean local field, with some features resembling those of classical ordinary differential equations. Here we consider equations of this kind, but with a weak degeneration. Under various assumptions, we prove the local existence and uniqueness of mild solutions, existence of their global extensions and a regularity property.
Keywords
Cite
@article{arxiv.2203.06623,
title = {Pseudo-Differential Equations with Weak Degeneration for Radial Functions of $p$-adic Argument},
author = {Alexandra V. Antoniouk and Anatoly N. Kochubei and Mariia V. Serdiuk},
journal= {arXiv preprint arXiv:2203.06623},
year = {2023}
}