Résurgence des solutions BKW d'une EDO singulièrement perturbée

Details Résurgence des solutions BKW d'une EDO singulièrement perturbée Résurgence des solutions BKW d'une EDO singulièrement perturbée

2006-01-31

arxiv.org/abs/math/0601773v1

Pr\'{e}pub. Math. Angers, 219 (2006)

Mathematics

Complex Variables

41 pages

Scientific paper

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.

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