Opuscula Math. 35, no. 5 (2015), 595-624
http://dx.doi.org/10.7494/OpMath.2015.35.5.595

Opuscula Mathematica

# On the summability of divergent power series solutions for certain first-order linear PDEs

Masaki Hibino

Abstract. 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.

Keywords: partial differential equation, divergent power series, summability, asymptotic expansion, analytic continuation, integro-differential equation, integral equation.

Mathematics Subject Classification: 35C20, 35C10, 35C15.

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