Structure of solutions of nonlinear partial differential equations of Gérard-Tahara type

Hidetoshi Tahara, Hiroshi Yamazawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let us consider the following nonlinear singular partial differential equation (t∂/∂t)m u = F(t, x, {(t∂/∂t) j (∂/∂x)α u} j+|α|≤m,j<m) in the complex domain. When the equation is of Fuchsian type with respect to t, holomorphic and singular solutions were investigated quite well by Gérard-Tahara under some assumptions on characteristic exponents. In this paper, the same type of equations is solved in the general case without any assumption on characteristic exponents.

Original languageEnglish
Pages (from-to)339-373
Number of pages35
JournalPublications of the Research Institute for Mathematical Sciences
Volume41
Issue number2
DOIs
Publication statusPublished - 2005 Jul

ASJC Scopus subject areas

  • Mathematics(all)

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