Le prolongement analytique de la solution du problème de Cauchy pour un certain opérateur différentiel à coefficients polynomiaux III

摘要

In part II of this series [To appear in J. Fixed Point Theory Appl. 14], we have studied analytic continuation and global structure of singularities of the solution of the Cauchy problem with meromorphic data for certain differential operators with principal part of polynomial coefficients in the complex domain. On the other hand, by a classical result of asymptotic development, we obtain a local expression of this solution. In this paper, we study an analytic continuation of this local solution. This gives a complement of part II.