Opuscula Math. 35, no. 5 (2015), 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

Hiroshi Yamazawa
Masafumi Yoshino

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.

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• Hiroshi Yamazawa
• Shibaura Institute of Technology, College of Engineer and Design, Minuma-ku, Saitama-shi, Saitama 337-8570, Japan
• Masafumi Yoshino
• Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8526, Japan
• Communicated by Theodore A. Burton.
• Revised: 2015-03-19.
• Accepted: 2015-03-20.
• Published online: 2015-04-27.