Pseudo-Differential Equations with Weak Degeneration for Radial Functions of \(p\)-adic Argument

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 c...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Antoniouk, Alexandra V, Kochubei, Anatoly N, Serdiuk, Mariia V
Format: Article
Language:English
Subjects:
Degeneration
Differential equations
Mathematical analysis
Mathematical functions
Ordinary differential equations
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2203.06623