Solvability of partial differential equations of nonlinear totally characteristic type with resonances
type: Item
instance of: scholarly article
title: Solvability of partial differential equations of nonlinear totally characteristic type with resonances
zbMATH Open document ID: 1061.35009
author: Hidetoshi Tahara
published in: Journal of the Mathematical Society of Japan
publication date: 2004-03-21T00:00:00Z
review text: The author considers the following nonlinear singular partial differential equation \[ (t\partial/ \partial t)^mu=F(t,x, \{(t \partial/ \partial t)^j(\partial/ \partial x)^\alpha u)_{j+|\alpha |\leq m,j<m} \}) \] in the complex domain. When the equation is of totally characteristic type, he proved already with H. Chen the existence of the unique holomorphic solution provided that the equation satisfies the Poincaré condition and that no resonances occur. In this paper he solves the same equation in the case where some resonances occur.
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35B34
zbMATH DE Number: 2061124
zbMATH Keywords: analytic continuation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Fuchsian type equation
reviewed by: Kunihiko Kajitani
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191418766
OpenAlex ID: W2039620812
DOI: 10.2969/JMSJ/1191418766
description: scientific article; zbMATH DE number 2061124