Small divisor problems and divergent formal power series solutions
type: Item
instance of: scholarly article
title: Small divisor problems and divergent formal power series solutions
zbMATH Open document ID: 0924.35021
author: Masafumi Yoshino
published in: Journal of the Mathematical Society of Japan
publication date: 1999-11-04T00:00:00Z
review text: We study small divisor phenomenon appearing in a semilinear Goursat problem without assuming any diophantine conditions. We can easily see that there appear divergent formal power series solutions in the class of analytic functions, and that the problem is not well posed in the class of smooth functions. We will show that for any divergent solution there exists a smooth solution whose Taylor expansion (at the origin) is equal to a divergent one under nonresonant condition. Because we assume no diophantine condition the generalized implicit function theorem cannot be applied. Instead of this, we reduce the problem to an elliptic boundary value problem in a corner domain. We can also show the alternatives for non well-posed problems.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 35R25
zbMATH DE Number: 1336899
zbMATH Keywords: nonresonant condition
zbMATH Keywords: no diophantine condition
zbMATH Keywords: Goursat problem
zbMATH Keywords: Riemann-Hilbert factorization
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05040903
OpenAlex ID: W2086489356
DOI: 10.2969/JMSJ/05040903
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description: scientific article; zbMATH DE number 1336899