Tohoku Mathematical Journal
2003
December
SECOND SERIES VOL. 55, NO. 4

Tohoku Math. J.
55 (2003), 477-485

Title SUR LE PROLONGEMENT ANALYTIQUE DE LA SOLUTION DU PROBLÈME DE CAUCHY POUR CERTAINS OPÉRATEURS DIFFÉRENTIELS DE PARTIE PRINCIPALE À COEFFICIENTS POLYNOMIAUX

Dédié à Professeur Norio Shimakura
Author Yûsaku Hamada

(Received September 4, 2001, revised July 26, 2002)
Abstract. In our preceding articles, by applying the results of Bieberbach, Fatou and Picard, we have constructed an example such that the domain of holomorphy of the solution admits an exterior point. Next we have studied the domain of holomorphy of the solution for differential operators with polynomial coefficients that concern the differential equations of Darboux-Halphen, of Chazy and of the modular function. In this article, we make some studies on the analytic continuation of the solution of the Cauchy problem for certain differential operators of principal part with polynomial coefficients.

2000 Mathematics Subject Classification. Primary 35A20; Secondary 34A20.
Key words and phrases. Cauchy problem, analytic continuations.

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