On multisummability of formal solutions with logarithm terms for some linear partial differential equations

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In this paper we consider formal solutions of the following form for some linear partial differential equations: û(t, x) = ∑i≥1k≤mi ui, k(x)ti (log t)k. Under the same conditions as those in Ōuchi [8], we show multisummability of the formal solutions û(t, x). It is our key of proofs to find a solution of exponential growth for convolution equations with polynomial coefficients with respect to y via the change of variable log t = y.

Original languageEnglish
Pages (from-to)371-406
Number of pages36
JournalFunkcialaj Ekvacioj
Issue number3
Publication statusPublished - 2017 Jan 1



  • Asymptotic expansion
  • Formal solutions
  • Multisummability

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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