Résurgence des solutions BKW d'une EDO singulièrement perturbée

Jean-Marc Rasoamanana (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

In this article, we investigate the resurgent properties of the WKB solutions for a singularly perturbated second order ordinary differential equation. In particular, we extend and propose a new proof of a theorem due to Aoki (et al) near a simple turning point, in the framework of the exact WKB analysis. Our scheme of proof is based on a Laplace-integral representation derived from an existence theorem of holomorphic solutions for a linear singular partial differential equation.

Mots clés: Equations différentielles ordinaires; équation de Schrödinger stationnaire; méthode BKW complexe; résurgence; phénomènes de Stokes

Domaines: Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]

Jean-Marc Rasoamanana. Résurgence des solutions BKW d'une EDO singulièrement perturbée. 2006. ⟨hal-00018339⟩