Borel Summability of Divergent Solutions for Singular First Order Linear Partial Differential Equations with Polynomial Coefficients

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 2, Page 279--309.

Hibino, Masaki
Borel Summability of Divergent Solutions for Singular First Order Linear Partial Differential Equations with Polynomial Coefficients
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Abstract:
This paper is concerned with the study of the Borel summability of divergent power series solutions for singular first order linear partial differential equations of nilpotent type. The conditions under which formal solutions are Borel summable are given by analytic continuation properties and growth (or decreasing) estimates for coefficients.

Mathematics Subject Classification (2000): Primary 35C20; Secondary 35C10, 35C15
Mathematical Reviews Number: MR1987134

Received: 2002-02-18