A linear Fuchsian equation with variable indices - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2003

A linear Fuchsian equation with variable indices

Résumé

We construct three types of solutions for a Fuchsian equation with variable indices: (1) branched solutions involving logarithms of the time variable $t$; (2) solutions involving $t^x$, where $x$ is a space variable; and, (3) for a model case, exact solutions involving hypergeometric functions. These three solutions have completely different singularities. The constructions are given in a form suitable for application to more general equations. As an illustration, we resolve in particular an apparent discrepancy between two recent results on this problem.

Dates et versions

hal-00002595 , version 1 (19-08-2004)

Identifiants

Citer

Ali Bentrad, Satyanad Kichenassamy. A linear Fuchsian equation with variable indices. Journal of Differential Equations, 2003, 190, pp.64-80. ⟨10.1016/S0022-0396(03)00029-9⟩. ⟨hal-00002595⟩
52 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More