Differential equations with degeneration and resurgent analysis
type: Item
instance of: scholarly article
title: Differential equations with degeneration and resurgent analysis
zbMATH Open document ID: 1221.34153
DOI: 10.1134/S0012266110090041
author: M. V. Korovina
author: Victor Shatalov
published in: Differential Equations
publication date: 2011-04-01T00:00:00Z
review text: The paper is devoted to the study of asymptotic expansions for degenerate elliptic equations of the form \(H(-r^{2}(d/dr), r)u=f\), where \(H(p,r):B_{1} \rightarrow B_{2}\) is an operator valued symbol, \(B_{1}, B_{2}\) are Banach spaces. The symbol \(H\) is polynomial in \(p\) and analytic in \(r\) in some neighborhood of \(r=0\). Endless continuability of the solutions is proven and their asymptotic expansions are obtained, firstly in the scalar case, \(B_{1}=B_{2}=\mathbb{C}\), and next in the general case of Fredholm equations with endless continuable right hand side. A main tool in this study is the resurgent analysis developed by J. Ecalle in the eighties of the last century.
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34M30
zbMATH DE Number: 5873481
zbMATH Keywords: degenerate elliptic equations
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: resurgent analysis
zbMATH Keywords: endless continuation
MaRDI profile type: Publication
cites work: Q4247385
cites work: Q4888891
description: scientific article; zbMATH DE number 5873481