Opuscula Mathematica
Opuscula Math. 35, no. 5 (), 825-845
http://dx.doi.org/10.7494/OpMath.2015.35.5.825
Opuscula Mathematica

Parametric Borel summability for some semilinear system of partial differential equations



Abstract. In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \(n\) independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.
Keywords: Borel summability, singular perturbation, Euler type operator.
Mathematics Subject Classification: 35C10, 45E10, 35Q15.
Cite this article as:
Hiroshi Yamazawa, Masafumi Yoshino, Parametric Borel summability for some semilinear system of partial differential equations, Opuscula Math. 35, no. 5 (2015), 825-845, http://dx.doi.org/10.7494/OpMath.2015.35.5.825
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.