Open AccessOn the summability of divergent power series solutions for certain first-order linear PDEs
Author(s) -
Masaki Hibino
Publication year - 2015
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2015.35.5.595
Subject(s) - mathematics , order (exchange) , power series , series (stratigraphy) , power (physics) , mathematical analysis , paleontology , physics , finance , economics , quantum mechanics , biology
This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations